The Double Bubble Problem on the Flat Two-Torus

2003/08/27 by Corneli, Joseph, Holt, Paul, Lee, George +3
#49Q10 #53A10 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.math/0308262

Abstract

We characterize the perimeter-minimizing double bubbles on all flat two-tori and, as corollaries, on the flat infinite cylinder and the flat infinite strip with free boundary. Specifically, we show that there are five distinct types of minimizers on flat two-tori, depending on the areas to be enclosed.

Related

• The double-bubble problem on the square lattice
• An elementary proof for the Double Bubble problem in ℓ¹ norm
• The Double Bubble Problem in the Hexagonal Norm
• 1D Triple Bubble Problem with Log-Convex Density
• The ℓ₁ double-bubble problem in three dimensions