61. Knotty Four-decade-old Math Problem Solved By Team Including UGA Professor Mathematicians Prove Double Soap Bubble Had It Right (March 20, proof of thedouble bubble conjecture that the familiar double soap bubble is the http://www.sciencedaily.com/releases/2004/11/041123211042.htm

@import "/styles/navbar.css"; @import "/styles/tabStyles.css"; Set home page Bookmark site Add search Latest News ... Email to friend Text Size A A A Front Page ... Advertise With Us Source University Of Georgia Date Print this page Email to friend Knotty Four-decade-old Math Problem Solved By Team Including UGA Professor It's not as famous as Fermat's Last Theorem. In fact, the math problem, which has not had a correct solution since it was proposed in the 1960s, doesn't even have a name. But a new, elegant solution for the unnamed 40-year old problem has intrigued scientists enough to be published in a two-part paper in one of the world's top math journals. Related News Stories Purdue Mathematician Claims Proof For Riemann Hypothesis (June 9, 2004) A Purdue University mathematician claims to have proven the Riemann hypothesis, often dubbed the greatest unsolved problem in ... full story UF Psychologists: Computer Anxiety New Illness Of High-Tech Age (July 31, 1998) full story Mental Math Dependant On Language, Researchers Find (October 16, 2001) full story Mathematicians Prove Double Soap Bubble Had It Right (March 20, 2000)

62. As últimas Do Mundo Da Matemática Here we announce a proof HMRR of the general double bubble conjecture in R3,using stability See also Frank Morgan double bubble conjecture Proved http://www.mat.uc.pt/~jaimecs/ult/ult.html

Novo recorde: 39th Known Mersenne Prime Found!! Millennium Prize Problems Goldbach's Conjecture: $1,000,000 challenge Double Bubble Conjecture Proved Novo recorde: GIMPS Finds Its Fourth Prime!!!! Robert J. Harley's Group Solves Elliptic Curve Cryptosystem Exercise Leibniz's 333-year-old problem solved de Archimedes Fields Medalists / Nevanlinna Prize 1998 ten consecutive primes in arithmetic progression 37th Known Mersenne Prime Discovered!!! New Math. Record: primes in arithmetic progression BEAL'S CONJECTURE Falso alarme: CARMICHAEL'S CONJECTURE FILIP SAIDAK PROVES CARMICHAEL'S CONJECTURE New Amicable Pair record 2^2976221-1 is the 36th known Mersenne prime Erdos Numbers update TIMSS - Executive Summary GIMPS Discovers 35th Mersenne Prime O maior ICOSAEDRO do mundo Paul Erdos morreu dia 20/9/96 Novo recorde: 39th Known Mersenne Prime Found!! -1 is now the Largest Known Prime December 6, 2001 > Michael Cameron, a 20 year-old volunteer in a worldwide research project called the Great Internet Mersenne Prime Search (GIMPS) , has discovered the largest known prime number using his PC and software by George Woltman and Entropia, Inc.

63. Kempner Colloquium Abstracts (Spring 2004) Title Proof of the double bubble conjecture Speaker Frank Morgan AffiliationWilliams College Time 230pm, Friday, April 2 Location EDUC 220 Abstract http://euclid.colorado.edu/~rmg/kempner/S04/abstracts.html

Kempner Colloquium Abstracts Spring 2004 Title: Constructing Wavelets from Generalized Filters Speaker: Kathy Merrill Affiliation: The Colorado College Time: 4:15pm, Monday, January 12 Location: BESC 180 Abstract: Over the past twenty years, wavelets have gained popularity as bases for transforms used in image and signal processing. This talk will begin with a brief introduction to how wavelets arise naturally in this context. We will then show how the tools of abstract harmonic analysis and spectral multiplicity theory can be used to build and classify wavelets. In particular, we present results from joint work with L. Baggett, P. Jorgensen, H. Medina and J. Packer that extend the classical techniques of Mallat and Meyer to construct wavelets using generalized multi-resolution analyses and generalized filters. Title: Computing limiting stationary distributions of small noisy networks Speaker: Fred Richman Affiliation: Florida Atlantic University Time: 4:15pm, Monday, January 26 Location: BESC 180 Abstract: The dynamics of opinion transformation is modeled by a neural network with a nonnegative matrix of connections. Noise is introduced at each site, and the limit of the stationary distributions of the resulting Markov chains as the noise goes to zero is taken as an indication of what configurations will be seen. An algorithm for computing this limit is given, and a number of examples are worked out. Some of the mathematical ideas developed, such as visible states, time scales, and a calculus of indexed probabilities, are of independent interest.

64. Stanford University Geometric Analysis Seminar 1999-2000 Abstract The double bubble conjecture states that the leastarea way to encloseand separate 2 given volumes in R^3 is the standard double bubble , http://math.stanford.edu/~moore/ga-sem99-00.html

Stanford University Geometric Analysis Seminar 1999-2000 Unless otherwise noted, all seminars begin at 4:00 pm in room 380-381T, and last approximately one hour. There is tea at 3:30 in the lounge area on the third floor of the Math Department Building (Building 380). Spring 2000 Schedule March 29 Tobias Ekholm, Stanford University Title: Total curvatures of holonomic links Abstract: April 5 Jingyi Chen, University of British Columbia, Vancouver, Canada Title: Holomorphic connections and lagrangian cycles Dinner: We will be taking the speaker out to dinner at a nearby restaurant after the seminar. April 12 Dan Ostrov, Santa Clara University Title: Determining shapes from discontinuous shading data and solving related first order PDEs where the flux function is discontinuous Abstract: Shape from shading is the study of how to determine a 3-D surface from a 2-D picture of the surface (plus as minimal an amount of additional information as possible.) When the picture has discontinuities (i.e., a bright part of the picture borders a darker part), difficulties arise in determining existence, uniqueness, and a method of computation for the solution of the underlying PDE describing the surface. We will explain a method of resolving these questions involving a control theory representation for the PDE, which will also allow us to answer larger questions about much more general first order PDEs with discontinuous flux/Hamiltonian functions. Dinner: We will be taking the speaker out to dinner at a nearby restaurant after the seminar.

65. WPI Department Of Mathematical Sciences - 1999-2000 Events In both talks, he described recent results on the double bubble conjecture, whichsays that the familiar double soap bubble is the leastarea way to enclose http://www.wpi.edu/Academics/Depts/Math/News/Events/9900.html

Department of Mathematical Sciences About Us Undergraduate Programs Graduate Programs ... About WPI Related Sites 1999-2000 Events Commencement more photos. Mathematical Sciences Awards Ceremony Marcus Sarkis , and a team composed of Jovanna Baptista, Larissa Gilbreath, and Robert Jaeger received the CIMS MQP Award for their project "Pricing a Waiver of Premium Upon Disability," advised by Ann Wiedie and sponsored by John Hancock Insurance Company . Other participating teams and their projects were Andre Freeman and Matthew Lavoie, "Comparing Heuristics for the Traveling Salesman Problem," advised by Brigitte Servatius , and Elizabeth Hogan and Nicholas Allgaier, "Credibility Analysis for Automobile Cession Strategies," advised by Arthur Heinricher and sponsored by Premier Insurance of Massaschusetts. Jonathan Moussa and Matt Shaw were recognized for their strong performance on the Putnam exam, and two teams composed of Brian Ball, Jonathan Moussa, and James Stickney and Jon Kennedy, Will Kennerly, and Casey Richardson, respectively, were recognized for honors received in the COMAP 2000 Mathematical Contest in Modeling. See news item Undergraduates score in Math Modeling, Putnam competitions

66. WPI Department Of Mathematical Sciences - Colloquia 1999-2000 The double bubble conjecture says that the familiar double soap bubble, Student Talk News on the double bubble conjecture, including work by http://www.wpi.edu/Academics/Depts/Math/News/Colloquia/9900.html

Department of Mathematical Sciences About Us Undergraduate Programs Graduate Programs ... About WPI Related Sites Colloquia 1999-2000 Adam Ding, Northeastern University, September 24 1999 11:00 a.m., Stratton Hall, Room 202; refreshments at 10:30 a.m. in the department lounge, SH107. Title: Study of Association in Bivariate Current Status Data Abstract: Current status data, also called interval censored data, Case 1, contains only information whether a failure happened or not at a random monitoring time. This type of data arise commonly in many studies of epidemiology, biomedicine, demography and reliability. While in its univariate setting, the estimation of the failure time distribution has been studied extensively, there has not been much research in the bivariate setting. When there are two failure times, say for example, development of hytertension and cardiovasular disease, we would like to study the relationship between them. Nonparametric estimation of the joint failure time distribution is not possible because of nonidentifiablity. A semiparametric approach as proposed to study the association between the two failure time variables. Nonparametric testing for the independence between two failure time variables is also explored. Peter Mueller,Institute of Statistics and Decision Sciences Duke University, October 8 1999

67. Loyola Math Club (I Was Wrong, The Logo Could Be Tackier) Hello Work of Frank Morgan and his undergraduate students led to the 2000 proof of thedouble bubble conjecture in R3 and extensions to other spaces. http://www.math.luc.edu/MathClub/

68. Schedule For The Nebraska Conference For Undergraduate Women In Mathematics Popping Bubbles the double bubble conjecture in the Fourth Dimension. Burnett 107Andrea Saunders, Representing Chemical Transformations with Transitional http://www.math.unl.edu/~ncuwm/2ndAnnual/schedule.html

Schedule for February 11-13, 2000 Friday, February 11, 2000 2:30 p.m. Welcome and Registration, Heritage Room, Nebraska Union There will be soft drinks and snacks at the registration. 3:30 p.m. Opening Session, Nebraska Union Auditorium Welcome: Judy Walker, Chair of the Conference Organizing Committee Opening Remarks: Merlin Lawson, Dean of Graduate Studies 3:45 - 4:45 p.m. Plenary Session, Nebraska Union Auditorium Karen Uhlenbeck, University of Texas "Solitons: Where applied math meets algebra and geometry" 4:45 - 5:00 p.m. Move to Burnett 5:00 p.m. Session 1 - Presentations by Undergraduate Women 5:00 - 5:15 p.m. Burnett 103: Sarah Brown, Cayley Graphs, Spectra of Cayley Graphs of Z/nZ, and Applications Burnett 107: Tracy Phelps, Analyzing Current Meter Data to Characterize Tidal and Subtidal Processes in Delaware's Inland Bays 5:20 - 5:35 p.m. Burnett 103: Holly Marie Swisher, Irreducibles in Block Semigroups Burnett 107: Teresa Selee

69. Elsevier.com - Geometric Measure Theory Soap Bubble Clusters. Proof of double bubble conjecture. The Hexagonal Honeycomband Kelvin Conjectures. Immiscible Fluids and Crystals. http://www.elsevier.com/wps/product/cws_home/675494

Home Site map Regional Sites Advanced Product Search ... Geometric Measure Theory Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book related information Submit your book proposal Other books in same subject area About Elsevier Select your view GEOMETRIC MEASURE THEORY A Beginner's Guide To order this title, and for more information, go to http://books.elsevier.com/bookscat/links/details.asp?isbn=0125068514 Third Edition By Frank Morgan , Williams College, Williamstown, Massachusetts, U.S.A. Description Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology. This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.

70. CSU- Fresno Math Department Colloquia will speak on Double Bubbles Minimize at 4105pm in Science 145. proved lastyear the double bubble conjecture which answered a question that had http://zimmer.csufresno.edu/~cleary/colloq/oldcolloq.html

Math Department Colloquia The Math Department Colloquia are a series of talks intended for a general audience. Everyone is encouraged to attend and the talks are directed at people who have a reasonable comprehension of the topics in undergraduate mathematics. Come meet our undergraduates, graduate students and faculty as well as our distinguished guest speakers. Colloquia from 1996-1997 academic year: Monday, May 5 Rescheduled: Monday, May 5, 3pm Dr. Joel Hass from the UC Davis Department of Mathematics will speak on "Double Bubbles Minimize" at 4:10-5pm in Science 145. There will be refreshments beforehand. Abstract: Dr. Hass will be speaking about the mathematical models of soap films and bubbles, which are modeled by minimal surfaces and constant mean curvature surfaces respectively. Dr. Hass, with his collaborator Roger Schlafly, proved last year the "Double Bubble Conjecture" which answered a question that had been first asked 2000 years ago and had been studied by many great mathematicians throughout history. He will be speaking about some of the innovative techniques used in this important work and will have some computer graphics as well as soap bubbles to illustrate the ideas. Monday April 21 3:10pm in Science 145: Sean Cleary , from the CSU -Fresno Mathematics Department will show the 20 minute video Not Knot , produced by the Geometry Center at the University of Minnesota. There will be a short explanatory talk in conjuntion with the video presentation. "Not Knot" is a computer-generated video which illustrates some important ideas from knot theory and hyperbolic geometry.

71. Notes From The Lab - MIT News Office Yvonne Lai, a junior in mathematics, has helped extend a recent mathematicalproof of the double bubble conjecture to four dimensions. http://web.mit.edu/newsoffice/2000/labnotes-0426.html

Skip to content massachusetts institute of technology news office advanced search news recent research campus by topic ... archives services request images subscribe submit news promote news ... media inquiries about us news office info MIT background contact Notes from the Lab Shelley Lauzon, WHOI April 26, 2000 FOUR-DIMENSIONAL PROOF Yvonne Lai, a junior in mathematics, has helped extend a recent mathematical proof of the "double bubble conjecture" to four dimensions. In a March address to the Undergraduate Mathematics Conference at the Rose-Hulman Institute of Technology, mathematicians from Williams College, Stanford University and the University of Granada announced their proof that the familiar double soap bubble is indeed the optimal shape for enclosing and separating two chambers of air. In a postscript, a group of undergraduates from Stanford, Williams and MIT including Ms. Lai extended the theorem to four-dimensional bubbles. Working last summer at Williams, they found a way to extend the proof to 4-space and certain cases in 5-space and above. Their work was part of the Research Experiences for Undergraduates sponsored by the National Science Foundation and Williams College. The group's paper on their work is awaiting publication. METALS FOUND IN BOSTON HARBOR Caroline Tuit, a graduate student in the MIT/Woods Hole Oceanographic Institution Joint Program, is co-author of a study that reveals high levels of platinum and palladium in Boston Harbor surface sediments. The researchers say the most likely source of these metals is the use of catalytic converters in cars, as well as industrial waste entering the harbor through the sewage system.

72. Abstract For Frank Morgan's Colloquium Soap Bubble Geometry. Frank Morgan Department of Mathematics and Ros of thedouble bubble conjecture, in which undergraduates have played an important http://dept.physics.upenn.edu/colloquium/abstract_morgan.html

Soap Bubble Geometry Frank Morgan Department of Mathematics Williams College Soap bubbles are round, and more complicated soap bubble clusters and other materials have other beautiful shapes. They apparently try to minimize surface area or energy. Are their shapes really the best possible? The presentation will include demonstrations and a description of the recent proof with Hutchings, Ritore', and Ros of the Double Bubble Conjecture, in which undergraduates have played an important role.

73. Greater Hudson Valley Mathematical Speakers Bureau, 1999-00 Academic Year The Double Soap Bubble Conjecture SPEAKER Frank Morgan AFFILIATION Williams The double bubble conjecture says that the familiar double soap bubble http://pages.slc.edu/~dking/GHVMSB.html

Greater Hudson Valley Mathematical Speakers Bureau The Greater Hudson Valley Mathematical Speakers Bureau, formed among liberal arts colleges in eastern New York, Connecticut and western Massachusetts, provides member institutions a source of undergraduate-level talks given by talented mathematicians residing at nearby colleges. In addition to providing interesting, accessible talks for undergraduates, the Bureau provides an opportunity for faculty members of neighboring colleges to interact and discuss common research or pedagogical interests. Current GHVMSB institutions: Bard College, Mount Holyoke College, Skidmore College, Sarah Lawrence College, Smith College, Trinity College, Union College, Vassar College and Williams College. If you have any questions or suggestions regarding the GHVMSB, please contact Dan King at Sarah Lawrence College (dking@mail.slc.edu). Please note: Edith Starr, GHVMSB co-organizer, of Vassar College is on sabbatical this year. List of available speakers for 1999-00 Academic Year Below is the GHVMSB's listing of available speakers and their talks for the 1998-00 academic year. Host institutions are encouraged to contact the speakers listed below directly to make specific arrangements regarding date and time of talk, directions for travel, equipment needs and honorarium amount.

74. Trailing After Double Bubbles: Science News Online, Jan. 29, 2000 A proof of the doublebubble conjecture for the case in which the two bubbles volumes are unequal appears within reach. http://www.sciencenews.org/articles/20000129/note17ref.asp

Science News Books. Subscribe to Science News ... Science News for Kids Math Trek The Math Game Food for Thought Sickening Food Science Safari Let's Go to Lascaux TimeLine 70 Years Ago in Science News Science News e-LETTER. ... Week of Jan. 29, 2000; Vol. 157, No. 5 Trailing after double bubbles Ivars Peterson A proof of the double-bubble conjecture for the case in which the two bubbles' volumes are unequal appears within reach. References: Morgan, F. 2000. The double bubble conjecture. Abstracts of Papers Presented to the American Mathematical Society 21(January):129. Further Readings: Morgan, F. 2000. The Math Chat Book . Washington, D.C.: Mathematical Association of America. Peterson, I. 1995. Toil and trouble over double bubbles. Science News 148(Aug. 12):101. Sources: Michael Hutchings Department of Mathematics Stanford University Stanford, CA 94305 Frank Morgan Department of Mathematics Williams College Williamstown, MA 01267 Web site: http://www.williams.edu:803/Mathematics/fmorgan/ Manuel Ritoré Departmento de Geometria y Topologia Universidad de Granada E-18071 Granada Spain Web site: http://www.ugr.es/~ritore/

75. MAA-NJ Spring 2001 Meeting double bubbles Proof and Prizes. Frank Morgan, Williams College. We ll reporton the 2000 proof of the double Soap bubble conjecture and http://orion.ramapo.edu/~ldant/old/rowan01/programs01.html

The Mathematical Association of America New Jersey Section - Spring Meeting Rowan University,Glassboro, NJ Saturday,April 21, 2001 Main Lecture Hall - Bosshart 203 Announcements Registration and Coffee - Second floor Lobby Bosshart Hall Book Exhibits Welcome byRonald Czochor, Chairperson, Department of Mathematics, Rowan University Graph Products and Cannon Pairs Joseph Loeffler, The College of New Jersey Student Speaker Presider: Cathy Liebars, The College of New Jersey Effective 3-D Visualizations of High Level Mathematical Functions Bonita Saunders, National Institute of Standards and Technology Presider: Bonnie Gold, Monmouth University Remarks by Chair of MAA-NJ Judith Lenk, Ocean County College Intermission (Coffee and Book Exhibits) Concurrent Sessions Workshop on Active Learning , by Janet Caldwell, Rowan University Campbell Library Commons Room 126 MAA-NJ Contributed papers I Bosshart 118 MAA-NJ Contributed papers - II Bosshart 116 MAA-NJ Contributed papers - III Bosshart 129 MAA-NJ Contributed papers - IV Bosshart 236 Student Contributed papers - Bosshart 316 Lunch (Book Exhibits end at 1:30) and Discussion Tables Student Center Ballroom Mathematics as Empirical Science Doron Zeilberger, Temple University

76. Double Bubble Is No Trouble A major advance towards the twin prime conjecture The trouble was that,although the familiar double bubble configuration certainly satisfied all the http://pass.maths.org.uk/issue12/news/bubble/

about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Latest news Spaghetti breakthrough What happens to bent pasta? How to measure a million The risks in Who wants to be a millionaire? Not just knots: the secrets of khipu The Inka way of counting Machine prose A computer program that can learn languages A new time machine Take a journey to the limits of common sense Gene-ius The search for the maths gene Plus... more news from the world of maths Explore the news archive Subscribe to our free newsletter Get the ... posters! September 2000 News Double bubble is no trouble A standard double bubble Four mathematicians have finally confirmed that the familiar double soap bubble is indeed the best way to enclose two separate volumes of air. In a double bubble, the joining surface bulges a little into the larger of the two bubbles. The three surfaces meet along a circle at 120 o If the two bubbles enclose the same volume, the separating surface is flat.

77. Bubbles For 2 areas, a standard double bubble is shortest (early 90’s). To prove theplanar soap bubble conjecture for m =7 areas or the soap bubble conjecture http://mail2.sc.chula.ac.th/~wacharin/maths/bubbles.html

The Planar Soap bubble Problem: to find the least perimeter way to enclose and separate m regions of m given areas on the plane. For 1 area, a circle is shortest (late 19th century). For 2 areas, a standard double bubble is shortest (early 90’s). For 3 areas, it is still unproven but we believe that a standard triple bubble is shortest while these triple bubbles are not minimizing. Worldwide responses: "...even the case of triple bubble in the plane is still open...", CNN. "Will we live long enough to see the proof of the planar triple bubble conjecture?", Time. "How many more mathematicians have to die to get this done?", People. "Closing triple, hidden dragon", SONY classic picture. "...so frustrated. Do we really have to prove it?", Hustler. Results that actually happened: '75: Almgren: well defined the problem. '87: Bleicher: some sufficient conditions on geometry of minimizing bubbles. '92: Morgan: existence of minimizing bubbles. '93: Foisy,Alfaro,Brock,Hodges,Zimba: the standard doubble is uniquely minimizing. '94: Cox,Hutchings,Kim,Light,Mauer,Tilton: the standard triple bubble is best among those with connected regions.

78. Double Bubbles Minimize - Hass, Schlatly (ResearchIndex) The proof of this conjecture was announced by Hass, Hutchings and 2.double bubble and torus bubble One first has to find categories of surfaces. http://citeseer.ifi.unizh.ch/hass98double.html

Double Bubbles Minimize (1998) (Make Corrections) (3 citations) Joel Hass, Roger Schlafly Home/Search Context Related View or download: ucdavis.edu/~hass/equal.ps Cached: PS.gz PS PDF Image ... Help From: ucdavis.edu/~hass/bubbles (more) (Enter author homepages) Rate this article: (best) Comment on this article (Enter summary) Abstract: The classical isoperimetric inequality in R 3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120 o . 1 Introduction Double, double, toil and trouble, Fire burn and cauldron bubble. Macbeth Act 4, Scene 1, Line 10 In this paper we find the unique surface of... (Update) Context of citations to this paper: More ...243rv 2. The proof of this conjecture was announced by Hass, Hutchings and Schlafiy [12] in 1995. The complete paper recently appeared as and our presen tation is based on that paper.

79. Science : MATHEMATICS: Why Double Bubbles Form The Way They Do @ HighBeam Resear double bubble conjecture, which states that when two. soap bubbles come together,they form a double bubble in order to enclose the total volume with the http://static.highbeam.com/s/science/march172000/mathematicswhydoublebubblesform

Library Web Executives New! ... Customer Support Question / Keyword(s): Advanced Search Current Article: MATHEMATICS: Why Double Bubbles Form the Way They Do Start S Science March 17, 2000 ... MATHEMATICS: Why Double Bubbles Form the Way They Do MATHEMATICS: Why Double Bubbles Form the Way They Do Science; March 17, 2000; Cipra, Barry Cipra, Barry Science March 17, 2000 MATHEMATICS:Why Double Bubbles Form the Way They Do Barry Cipra An international team of mathematicians has announced a proof of the "double bubble" conjecture, which states that when two soap bubbles come together, they form a double bubble in order to enclose the total volume with the minimum surface area. By honing a new technique for analyzing the stability of competing shapes, the team has shown that only the standard shape is truly minimalany other, supposedly area-minimizing shape can be ever so slightly twisted into a shape with even less area, a contradiction that rules out these other candidates. MATHEMATICS:Why Double Bubbles Form the Way They Do Barry Cipra Need to entertain a child? Try blowing soap bubbles. Need to keep

80. [math/0208120] Double Bubbles In The 3-torus double bubbles in the 3torus. Authors Miguel Carrión-Álvarez (UC Riverside),Joseph Corneli We present a conjecture, based on computational results, http://arxiv.org/abs/math.DG/0208120

Mathematics, abstract math.DG/0208120 From: Genevieve Walsh [ view email ] Date: Thu, 15 Aug 2002 00:33:49 GMT (636kb) Double bubbles in the 3-torus Authors: (UC Riverside), Joseph Corneli (New College of Florida), Genevieve Walsh (UC Davis), Shabnam Beheshti (Texas Tech University) Comments: 13 pages, 4 figures. Prepared on behalf of the participants in the Clay Mathematics Institute Summer School on the Global Theory of Minimal Surfaces, held at the Mathematical Sciences Research Institute in Berkeley, California, Summer 2001 Subj-class: Differential Geometry; Geometric Topology MSC-class: We present a conjecture, based on computational results, on the area minimizing way to enclose and separate two arbitrary volumes in the flat cubic 3-torus. For comparable small volumes, we prove that an area minimizing double bubble in the 3-torus is the standard double bubble from R^3. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers?

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