Submitted Paper
Inserted: 3 may 2026
Last Updated: 9 may 2026
Year: 2026
Abstract:
We prove a heat semigroup characterization of the total variation for compactly supported ${\rm BV}$ functions 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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