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arXiv · 2010.12131

Yet another heat semigroup characterization of BV functions on Riemannian manifolds

Patricia Alonso Ruiz·Fabrice Baudoin
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Abstract

This paper provides a characterization of functions of bounded variation (BV) in a compact Riemannian manifold in terms of the short time behavior of the heat semigroup. In particular, the main result proves that the total variation of a function equals the limit characterizing the space BV. The proof is carried out following two fully independent approaches, a probabilistic and an analytic one. Each method presents different advantages.

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BibTeXRIS

Patricia Alonso Ruiz, Fabrice Baudoin. 2020-10-23. Yet another heat semigroup characterization of BV functions on Riemannian manifolds. https://arxiv.org/abs/2010.12131

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