Abstract
In the geometry and analysis on compact Riemannian manifolds, the Hopf maximum principle is a very useful tool. The Omori-Yau maximum principle is an important,basic and powerful tool on noncompact Riemannian manifolds corresponding to the Hopf maximum principle in the compact case.In this paper, we give a survey on the classical Omori-Yau maximum principle and its various generalizations, as well as their applications in the geometry and analysis on manifolds.
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