关于收缩或稳定的梯度Ricci孤立子的数量曲率估计的一个简要证明

摘要

收缩或稳定的梯度Ricci孤立子的数量曲率的下界估计对于研究势函数增长估计或者体积增长估计十分有用。文章利用光滑度量测度空间上的Laplace比较定理，得到数量曲率下界估计的一个简要证明。%The lower bound estimate for the scalar curvature of a shrinking or steady gradient Ricci soliton is very use-ful for studying the estimates of the growth of the potential function and the volume. In this paper , by using the Laplacian comparison theorem in smooth metric measure spaces , a simple proof of this scalar curvature estimate is obtained.