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December 2006 A priori upper bounds of solutions satisfying a certain differential inequality on complete manifolds
Kensho Takegoshi
Osaka J. Math. 43(4): 791-806 (December 2006).

Abstract

In this article we study a priori upper bounds of subsolutions satisfying a certain differential inequality (*) below on a non-compact complete Riemannian manifold $(M,g)$ without any Ricci curvature condition. Our method depends on a volume estimate of open subsets where those solutions satisfy a certain strong subharmonicity. Several applications in conformal deformation of metrics and value distribution of harmonic maps are given.

Citation

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Kensho Takegoshi. "A priori upper bounds of solutions satisfying a certain differential inequality on complete manifolds." Osaka J. Math. 43 (4) 791 - 806, December 2006.

Information

Published: December 2006
First available in Project Euclid: 11 December 2006

zbMATH: 1139.53021
MathSciNet: MR2303550

Subjects:
Primary: 53C20 , 53C21 , 53C43 , 58J05

Rights: Copyright © 2006 Osaka University and Osaka City University, Departments of Mathematics

Vol.43 • No. 4 • December 2006
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