Isoperimetric Regions in Anisotropically Scaled Product Manifolds

Efstratios Vernadakis

Isoperimetric Regions in Anisotropically Scaled Product Manifolds

Differential Geometry 2025-12-11 v1

Authors: Efstratios Vernadakis

Abstract

Let $M, N$ be compact Riemannian manifolds. Then, for fixed volume fraction, in the product of a sufficiently small homothetic copy of $M$ with $N$ , every isoperimetric region is the product of $M$ with an isoperimetric region in $N$ , provided the boundaries of the isoperimetric regions in $N$ are smooth.

Keywords

isoperimetric regions product manifolds anisotropic scaling Riemannian geometry homothetic copy volume fraction

Cite

@article{arxiv.2512.09490,
  title  = {Isoperimetric Regions in Anisotropically Scaled Product Manifolds},
  author = {Efstratios Vernadakis},
  journal= {arXiv preprint arXiv:2512.09490},
  year   = {2025}
}

Comments

15 pages

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