Omori-Yau极值原理及其应用

Omori-Yau maximum principles and their applications

在紧致Riemann流形上的几何与分析中,Hopf最大值原理是一个非常有用的工具.Omori-Yau极值原理是完备非紧Riemann流形上相应于紧致情形Hopf最大值原理的一个重要、基本而有力的工具.本文概述了经典的Omori-Yau极值原理以及它的各种推广,并给出它们在流形的几何与分析问题中的应用.

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.