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arXiv · 2108.03207

Isoperimetric inequalities in cylinders with density

Katherine Castro
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Abstract

Given a compact Riemannian manifold with density $M$ without boundary and the real line $\mathbb{R}$ with constant density, we prove that isoperimetric regions of large volume in $M\times\mathbb{R}$ with the product density are slabs of the form $M\times [a,b]$. We previously prove, as a necessary step, the existence of isoperimetric regions in any manifold of density where a subgroup of the group of transformations preserving weighted perimeter and volume acts cocompactly.

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Katherine Castro. 2021-08-06. Isoperimetric inequalities in cylinders with density. https://arxiv.org/abs/2108.03207

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