Parabolicity and stochastic completeness of manifolds in terms of the Green formula

Alexander Grigor'yan, Jun Masamune

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We present and prove new characterizations of parabolicity and stochastic completeness for a general weighted manifold M as well as the uniqueness of the Markov extensions of the Laplacian in terms of Green's formula. Moreover, we study the relationship between those properties and the singularity of M in terms of a fractal dimension and capacity.

Original languageEnglish
Pages (from-to)607-632
Number of pages26
JournalJournal des Mathematiques Pures et Appliquees
Volume100
Issue number5
DOIs
Publication statusPublished - 2013 Nov 1

Keywords

  • Conservation property
  • Green's formula
  • Heat kernel
  • Markov extensions
  • Non-explosion
  • Parabolicity
  • Primary
  • Recurrence
  • Riemannian manifold
  • Secondary
  • Self-adjoint extensions
  • Stochastic completeness
  • Weighted manifold

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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