Laplacian 比較定理及其應用

Abstract

比較定理主要是將任意可微分流形上的一些量與其他流形（如常數曲率流形）作比較。主要有均曲率， Hessian, Laplacian 及體積比較，並且有數種不同證明方法。 本文將敘述比較定理的內容以及其間的關係，並嘗試應用。

Comparison theorems are mainly to compare some quantities in an arbitrary di erential manifold with other manifolds (usually with space forms). The main comparisons are about mean curvature, Hessian, Laplacian and volume, and there are various ways of proof. In this paper, I would like state the theorems and relations between them, and try to give some applications.