In the unit cubic flat three-torus, every volume-minimizing region is a ball, a circular tube about a shortest closed geodesic, a coordinate slab or the complement of one of these, in the predicted volume ranges, including both types at the transition volumes 4π/81 and 1/π.
In the unit cubic flat three-torus, every volume-minimizing region is a ball, a circular tube about a shortest closed geodesic, a coordinate slab or the complement of one of these, in the predicted volume ranges, including both types at the transition volumes 4π/81 and 1/π.
In the unit cubic flat three-torus, every volume-minimizing region is a ball, a circular tube about a shortest closed geodesic, a coordinate slab or the complement of one of these, in the predicted volume ranges, including both types at the transition volumes 4π/81 and 1/π.
If correct, determines the complete isoperimetric profile and classifies all minimizers of the cubic flat three-torus.
Which regions minimize perimeter at each volume in the cubic flat three-torus?
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