Yet another heat semigroup characterization of BV functions on Riemannian manifolds

2020/10/23 by Patricia Alonso Ruiz, Ruiz, Patricia Alonso, Fabrice Baudoin +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Bayesian Methods and Mixture Models #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #RNA Research and Splicing #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2010.12131

openalex publication_date 2020/10/23 · openalex created_date 2023/08/31 · openalex updated_date 2026/07/28

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.

Related

• Functions with bounded variation on a class of Riemannian manifolds with Ricci curvature unbounded from below
• Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates
• Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates
• Two characterization of BV functions on Carnot groups via the heat semigroup
• Asymptotic behavior of the heat semigroup on certain Riemannian manifolds