Double Bubbles in the Three-Torus

Miguel Carrión Álvarez Department of Mathematics, 057, University of California, Riverside, CA, 92521-0135 E-mail: [email protected]

Joseph Corneli Department of Mathematics, University of Texas, Austin, TX, 78712 E-mail: [email protected]

Genevieve Walsh Department of Mathematics, University of Texas, Austin, TX, 78712 E-mail: [email protected]

Shabnam Beheshti Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003-9305 E-mail: [email protected]

Abstract

We present a conjecture, based on computational results, on the area-minimizing method of enclosing and separating two arbitrary volumes in the flat cubic three-torus, T ³. For comparable small volumes, we prove that the standard double bubble from R ³ is area-minimizing.

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Double Bubbles in the Three-Torus

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Double Bubbles in the Three-Torus

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