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Double Bubbles Minimize

Joel Hass·Roger Schlafly
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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.

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Joel Hass, Roger Schlafly. 2000-10-10. Double Bubbles Minimize. https://arxiv.org/abs/math/0003157

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