Family 354Differential geometryNo LeanNot yet digested
The isoperimetric profile of the cubic three-torus
Determines the isoperimetric profile of the unit cubic flat three-torus and classifies every finite-perimeter minimizer: balls, circular tubes around shortest closed geodesics, coordinate slabs, and their complements. The transition volumes are and , with exactly the adjacent two types minimizing at each transition.
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The Isoperimetric Conjecture for the Cubic Flat Three-Torus
Sep 24, 2026·article.pdf
We prove the isoperimetric conjecture for the cubic flat three-torus and classify all minimizers, including the equality cases at the transition volumes and . The minimizing regions are balls, circular tubes about shortest closed geodesics, coordinate slabs, and their complements.