Parabolicity, the divergence theorem for $\delta$-subharmonic functions and applications to the Liouville theorems for harmonic maps
Atsuji, Atsushi
Tohoku Math. J. (2), Tome 57 (2005) no. 1, p. 353-373 / Harvested from Project Euclid
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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.
Publié le : 2005-09-14
Classification:  Dirichlet form,  Martingale,  Harmonic map,  Liouville theorem,  $\delta$-subharmonic functions,  31C05,  58J65 
@article{1128703002,
     author = {Atsuji, Atsushi},
     title = {Parabolicity, the divergence theorem for $\delta$-subharmonic functions and applications to the Liouville theorems for harmonic maps},
     journal = {Tohoku Math. J. (2)},
     volume = {57},
     number = {1},
     year = {2005},
     pages = { 353-373},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1128703002}
}

Atsuji, Atsushi. Parabolicity, the divergence theorem for $\delta$-subharmonic functions and applications to the Liouville theorems for harmonic maps. Tohoku Math. J. (2), Tome 57 (2005) no. 1, pp.  353-373. http://gdmltest.u-ga.fr/item/1128703002/