English

Double Bubbles Minimize

Differential Geometry 2007-05-23 v2 Optimization and Control

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 degrees.

Keywords

Cite

@article{arxiv.math/0003157,
  title  = {Double Bubbles Minimize},
  author = {Joel Hass and Roger Schlafly},
  journal= {arXiv preprint arXiv:math/0003157},
  year   = {2007}
}

Comments

57 pages, 32 figures. Includes the complete code for a C++ program as described in the article. You can obtain this code by viewing the source of this article