Università degli Studi di Genova

A note on bounded variation and heat semigroup on Riemannian manifolds
Abstract: In a recent paper M. Miranda Jr. et al. have shown that the classical De Giorgi's heat kernel characterization of function of bounded variation on Euclidean space extends to Riemannian manifolds with Ricci curvature bounded from below and which satisfy a uniform lower bound estimate on the volume of geodesic balls of fixed radius. We give a shorter proof of the same result assuming only the lower bound on the Ricci curvature. Keywords: Riemannian manifolds, bounded variation, heat kernel MSC: 53, 49, 58, 47 Pubblicato su: Bulletin of the Australian Mathematical Society Vol. 76 (2007) N. 1 Pag. 155-160

A note on bounded variation and heat semigroup on Riemannian manifolds