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

Author(s): Kensho Takegoshi
Journal: Proc. Amer. Math. Soc. 131 (2003), 2849-2858.
MSC (2000): Primary 31B05, 35B05, 35J05, 35J60, 53C43
Posted: April 1, 2003
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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: 10.1090/S0002-9939-03-07042-4
PII: S 0002-9939(03)07042-4
Received by editor(s): April 9, 2002
Posted: April 1, 2003
Communicated by: Bennett Chow
Copyright of article: Copyright 2003, American Mathematical Society

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