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

2012/11/29 by Batu Güneysu, Güneysu, Batu, Diego Pallara +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR) #math.DG #math.MG #math.PR

paper · pdf · doi:10.48550/arxiv.1211.6863

26 pages; BV-characterization of Sobolev functions added

arxiv created 2013/01/24 · arxiv updated 2013/01/25

Abstract

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 L¹-functions to a class of Riemannian manifolds with possibly unbounded from below Ricci curvature.

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