Functions with bounded variation on a class of Riemannian manifolds with   Ricci curvature unbounded from below
  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. 
Batu G\"uneysu, Diego Pallara
math.DG math.MG math.PR