Obtuse constants of Alexandrov spaces
Differential Geometry
2018-05-10 v2 Metric Geometry
Abstract
We introduce a new geometric invariant called the obtuse constant of spaces with curvature bounded below. We first find relations between this invariant and the normalized volume. We also discuss the case of maximal obtuse constant equal to , where we prove some rigidity for spaces. Although we consider Alexandrov spaces with curvature bounded below, the results are new even in the Riemannian case.
Keywords
Cite
@article{arxiv.1710.00497,
title = {Obtuse constants of Alexandrov spaces},
author = {Ayato Mitsuishi and Takao Yamaguchi},
journal= {arXiv preprint arXiv:1710.00497},
year = {2018}
}
Comments
We have changed the definition of obtuse constants in the first vertion "Comaparison angles and volume" because of an error in the first verson