Open Access
October, 2019 Obtuse constants of Alexandrov spaces
J. Math. Soc. Japan 71(4): 1081-1103 (October, 2019). DOI: 10.2969/jmsj/78917891


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 $\pi/2$, 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.

Funding Statement

This work was supported by JSPS KAKENHI Grant Numbers 26287010, 15H05739, 15K17529.


Download Citation

Ayato MITSUISHI. Takao YAMAGUCHI. "Obtuse constants of Alexandrov spaces." J. Math. Soc. Japan 71 (4) 1081 - 1103, October, 2019.


Received: 1 October 2017; Revised: 11 April 2018; Published: October, 2019
First available in Project Euclid: 13 June 2019

zbMATH: 07174396
MathSciNet: MR4023297
Digital Object Identifier: 10.2969/jmsj/78917891

Primary: 53C20 , 53C21 , 53C23

Keywords: Alexandrov space , ideal boundary , normalized volume , obtuse constant

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 4 • October, 2019
Back to Top