English

Yet another heat semigroup characterization of BV functions on Riemannian manifolds

Functional Analysis 2020-10-26 v1 Analysis of PDEs Probability

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.

Keywords

Cite

@article{arxiv.2010.12131,
  title  = {Yet another heat semigroup characterization of BV functions on Riemannian manifolds},
  author = {Patricia Alonso Ruiz and Fabrice Baudoin},
  journal= {arXiv preprint arXiv:2010.12131},
  year   = {2020}
}