带边界流形上的 Ricci 流
微分几何
2015-04-14 v2
摘要
我们研究了带边界流形上 Ricci-DeTurck 方程边值解的短时存在性与正则性。基于此，我们证明了在给定边界平均曲率和共形类以及任意初始数据条件下，Ricci 流的短时存在性与唯一性。最后，我们确立了在适当控制边界数据的情况下，只要环境曲率和边界的第二基本形式保持有界，该流便可持续存在。
引用
@article{arxiv.1210.0813,
title = {The Ricci flow on manifolds with boundary},
author = {Panagiotis Gianniotis},
journal= {arXiv preprint arXiv:1210.0813},
year = {2015}
}
备注
Improved exposition and statement on the control of the existence time of the Ricci flow, and updated/added some references. Also, a new section is added, demonstrating a situation in which the existence time of the Ricci flow (with boundary) with flat initial data and well behaved boundary data may become arbitrarily small