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Mathematische Annalen

, Volume 363, Issue 3–4, pp 1307–1331 | Cite as

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

  • Batu Güneysu
  • Diego PallaraEmail author
Article

Abstract

After establishing some new global facts (like a measure theoretic structure theorem and a new invariant characterization of Sobolev functions) 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 \(\mathsf {L}^1\)-functions to a class of Riemannian manifolds with possibly unbounded from below Ricci curvature.

Mathematics Subject Classification

26B30 53C21 47D06 58J35 

Notes

Acknowledgments

B. G. has been financially supported by the SFB 647: Raum-Zeit-Materie. D. P. is member of the Italian Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and has been partially supported by PRIN 2010 M.I.U.R. “Problemi differenziali di evoluzione: approcci deterministici e stocastici e loro interazioni”.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Dipartimento di Matematica e Fisica Ennio De GiorgiUniversità del SalentoLecceItaly

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