Volume pinching theorems for CAT(1) spaces
Differential Geometry
2021-03-30 v3 Metric Geometry
Abstract
We examine volume pinching problems of CAT(1) spaces. We characterize a class of compact geodesically complete CAT(1) spaces of small specific volume. We prove a sphere theorem for compact CAT(1) homology manifolds of small volume. We also formulate a criterion of manifold recognition for homology manifolds on volume growths under an upper curvature bound.
Cite
@article{arxiv.1810.13056,
title = {Volume pinching theorems for CAT(1) spaces},
author = {Koichi Nagano},
journal= {arXiv preprint arXiv:1810.13056},
year = {2021}
}
Comments
A final version, modified the texts in Section 4