Ricci曲率下有界的非塌缩三维流形的Ricci流
微分几何
2009-12-01 v2 偏微分方程分析
摘要
我们考虑完备（可能非紧）的三维黎曼流形(M,g)，满足：a) (M,g)是非塌缩的，b) (M,g)的Ricci曲率下有界，c) (M,g)在无穷远处的几何结构并非极端。给定这样的初始数据(M,g)，我们证明Ricci流在短时间区间内存在。这使我们能够构造任意（可能奇异的）度量空间(X,d)的Ricci流，该空间作为一致满足a)、b)和c)的三维流形序列的Gromov-Hausdorff极限出现。作为推论，我们证明这样的X必定是一个流形。
引用
@article{arxiv.0903.2142,
title = {Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below},
author = {Miles Simon},
journal= {arXiv preprint arXiv:0903.2142},
year = {2009}
}
备注
Changes: V1 contained an incorrect use of the Hessian comparison theorem (in the section "Conformal deformations ..."). In v2 this is corrected. The condition at infinity for the non-compact case has been modified. There is a short new section:"Previous results". Minor reorganisation