关于非紧梯度里奇孤立子的注记
微分几何
2009-10-23 v3
摘要
在本文中，我们展示了如何利用来自随机分析的技术，例如随机完备性（以无穷远处弱极大值原理的形式）、抛物性和与势函数相关的加权拉普拉斯算子的 -刘维尔型结果，来获得在相关量的 条件下梯度里奇孤立子的平凡性、刚性结果以及标量曲率估计。
引用
@article{arxiv.0905.2868,
title = {Remarks on non-compact gradient Ricci solitons},
author = {Stefano Pigola and Michele Rimoldi and Alberto G. Setti},
journal= {arXiv preprint arXiv:0905.2868},
year = {2009}
}
备注
The main changes over the previous version are that Theorem 2 has been improved by removing the pointwise growth assumption on $|\nabla f|$ in the case $p=1$, and that in Theorem 3, a shrinking gradient Ricci soliton is shown to be isometric to $\R^m$ in the endpoint case $S_*=0$