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
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.
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