Metrics with non-negative Ricci curvature on convex three-manifolds
Differential Geometry
2016-10-19 v4 Geometric Topology
Abstract
We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphisms of the three-ball) is contractible. As an application, using results of Maximo, Nunes, and Smith [MNS13], we show the existence of properly embedded free boundary minimal annulus on any three-ball with non-negative Ricci curvature and strictly convex boundary.
Keywords
Cite
@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}
}
Comments
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