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September 2005 Parabolicity, the divergence theorem for $\delta$-subharmonic functions and applications to the Liouville theorems for harmonic maps
Atsushi Atsuji
Tohoku Math. J. (2) 57(3): 353-373 (September 2005). DOI: 10.2748/tmj/1128703002

Abstract

We show that the parabolicity of a manifold is equivalent to the validity of the 'divergence theorem' for some class of $\delta$-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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Atsushi Atsuji. "Parabolicity, the divergence theorem for $\delta$-subharmonic functions and applications to the Liouville theorems for harmonic maps." Tohoku Math. J. (2) 57 (3) 353 - 373, September 2005. https://doi.org/10.2748/tmj/1128703002

Information

Published: September 2005
First available in Project Euclid: 7 October 2005

zbMATH: 1136.31309
MathSciNet: MR2154099
Digital Object Identifier: 10.2748/tmj/1128703002

Subjects:
Primary: 31C05
Secondary: 58J65

Rights: Copyright © 2005 Tohoku University

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Vol.57 • No. 3 • September 2005
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