完备非紧流形上里奇流解的唯一性
微分几何
2011-10-10 v4 偏微分方程分析
摘要
我们利用De Turck方法证明了具有有界曲率的完备非紧流形上里奇流解的唯一性。作为推论，我们给出了具有有界曲率的完备非紧流形上里奇调和流解存在性的正确证明。
引用
@article{arxiv.0704.3468,
title = {Uniqueness of solutions of Ricci flow on complete noncompact manifolds},
author = {Shu-Yu Hsu},
journal= {arXiv preprint arXiv:0704.3468},
year = {2011}
}
备注
A simple example of a manifold with bounded curvature and injectivity radius going to zero as the point tends to infinity is given. A proof and argument why the crucial lemma Lemma 2.2 of the Chen-Zhu's paper \cite{CZ} cannot hold is given