Sets of finite perimeter on Riemannian manifolds and stochastic completeness
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913084827762688 |
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| author | Gennaioli, Luca |
| author_facet | Gennaioli, Luca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01979 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sets of finite perimeter on Riemannian manifolds and stochastic completeness Gennaioli, Luca Analysis of PDEs 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. |
| title | Sets of finite perimeter on Riemannian manifolds and stochastic completeness |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.01979 |