Manifolds tightly covered by two metric balls
Differential Geometry
2019-02-19 v2
Abstract
In this note we provide natural optimal geometric conditions for a Riemannian manifold suitably covered by two open metric balls to be homeomorphic to a sphere. This can be viewed as a geometric analogue of Brown's theorem in topology stating that a closed manifold covered by two topological balls is a sphere.
Cite
@article{arxiv.1610.08190,
title = {Manifolds tightly covered by two metric balls},
author = {Jianming Wan},
journal= {arXiv preprint arXiv:1610.08190},
year = {2019}
}
Comments
With the help of Karsten Grove, the submission is rewirtten. Add two theorems and more connections with previous literatures