Parabolicity, the divergence theorem for δ-subharmonic functions and applications to the liouville theorems for harmonic maps

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Abstract

We show that the parabolicity of a manifold is equivalent to the validity of the ‘divergence theorem’ for some class of δ-subharmonic functions. From this property we can show a certain Liouville property of harmonic maps on parabolic manifolds. Elementary stochastic calculus is used as a main tool.

Original languageEnglish
Pages (from-to)353-373
Number of pages21
JournalTohoku Mathematical Journal
Volume57
Issue number3
DOIs
Publication statusPublished - 2005 Jan 1

Keywords

  • Dirichlet form
  • Harmonic map
  • Liouville theorem
  • Martingale
  • δ-subharmonic functions

ASJC Scopus subject areas

  • Mathematics(all)

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