通过正则化 Ricci 流给出 $C^0$ 度量的逐点下标量曲率界
微分几何
2019-12-02 v3
摘要
在本文中，我们提出了一类对 度量良定义的弱下标量曲率界的局部定义。我们证明了如下结论：我们的定义在度量高于二阶的扰动下是稳定的；存在从 初始数据出发并在正时间光滑的 Ricci 流的合理概念；并且弱下标量曲率界在从 初始数据出发的 Ricci 流演化下得以保持。
引用
@article{arxiv.1907.13116,
title = {Pointwise lower scalar curvature bounds for $C^0$ metrics via regularizing Ricci flow},
author = {Paula Burkhardt-Guim},
journal= {arXiv preprint arXiv:1907.13116},
year = {2019}
}
备注
65 pages. v3: small errors corrected. This is a post-peer-review, pre-copyedit version of an article published in Geometric and Functional Analysis. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00039-019-00514-3