Sets of finite perimeter on Riemannian manifolds and stochastic completeness

Luca Gennaioli

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arXiv · 2605.01979

Sets of finite perimeter on Riemannian manifolds and stochastic completeness

Luca Gennaioli

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Abstract

We prove a heat semigroup characterization of the total variation for compactly supported ${\rm BV}$ on arbitrary smooth complete weighted Riemannian manifolds, extending the main result in \cite{GP15}. We then provide an example of a weighted manifold where such equivalence does not hold for a large class of sets of finite perimeter.

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Luca Gennaioli. 2026-05-03. Sets of finite perimeter on Riemannian manifolds and stochastic completeness. https://arxiv.org/abs/2605.01979

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