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

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1 Citation (Scopus)

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
Publication statusPublished - 2005 Sep

Fingerprint

Divergence theorem
Subharmonic Function
Liouville's theorem
Harmonic Maps
Stochastic Calculus
Class

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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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.",
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