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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on divergence of $L^{p}$-integrals of subharmonic functions and its applications


Author: Kensho Takegoshi
Journal: Proc. Amer. Math. Soc. 131 (2003), 2849-2858
MSC (2000): Primary 31B05, 35B05, 35J05, 35J60, 53C43
Published electronically: April 1, 2003
MathSciNet review: 1974342
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Abstract: A non $L^{p}$-integrability condition of non-constant non-negative subharmonic functions on a general complete manifold $(M,g)$ is given in an optimal form. As an application in differential geometry, several topics related to parabolicity of manifolds, the Liouville theorem for harmonic maps and conformal deformation of metrics are shown without any assumption on the Ricci curvature of $(M,g)$.


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Additional Information

Kensho Takegoshi
Affiliation: Department of Mathematics, Graduate School of Science, Machikaneyama-cho 1-16, Toyonaka-shi Osaka, 560-0043, Japan
Email: kensho@math.wani.osaka-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07042-4
PII: S 0002-9939(03)07042-4
Received by editor(s): April 9, 2002
Published electronically: April 1, 2003
Communicated by: Bennett Chow
Article copyright: © Copyright 2003 American Mathematical Society