Isoperimetric Regions in Anisotropically Scaled Product Manifolds

Efstratios Vernadakis

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arXiv · 2512.09490

Isoperimetric Regions in Anisotropically Scaled Product Manifolds

Efstratios Vernadakis

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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.

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BibTeX RIS

Efstratios Vernadakis. 2025-12-10. Isoperimetric Regions in Anisotropically Scaled Product Manifolds. https://arxiv.org/abs/2512.09490

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