凸三维流形上具有非负Ricci曲率的度量
微分几何
2016-10-19 v4 几何拓扑
摘要
我们证明具有非负Ricci曲率和严格凸边界的三球上光滑黎曼度规的空间是道路连通的；而且，相关的模空间（即模三球的保向微分同胚）是可缩的。作为应用，利用Maximo、Nunes和Smith [MNS13]的结果，我们展示了在任何具有非负Ricci曲率和严格凸边界的三球上存在适当嵌入的自由边界极小环面。
引用
@article{arxiv.1505.06789,
title = {Metrics with non-negative Ricci curvature on convex three-manifolds},
author = {Antonio Ache and Davi Maximo and Haotian Wu},
journal= {arXiv preprint arXiv:1505.06789},
year = {2016}
}
备注
Strengthened the conclusions in Theorems 1.1 and 1.2 that the respective moduli spaces are contractible; corrected typos; updated references. To appear in Geometry & Topology