Functions with bounded variation on a class of Riemannian manifolds with Ricci curvature unbounded from below

Batu Güneysu, Diego Pallara

Published 2012-11-29, updated 2013-01-24Version 2

After establishing some new global facts (like a measure theoretic structure theorem and approximation results) about complex-valued functions with bounded variation on arbitrary noncompact Riemannian manifolds, we extend results of Miranda/the second author/Paronetto/Preunkert and of Carbonaro/Mauceri on the heat semigroup characterization of the variation of L^1-functions to a class of Riemannian manifolds with possibly unbounded from below Ricci curvature.