A sphere theorem for 2-dimensional CAT(1)-spaces

Koichi Nagano

Vol. 206 (2002), No. 2, 401–424

DOI: 10.2140/pjm.2002.206.401

Abstract

We study sphere theorems for compact, geodesically complete 2-dimensional CAT(1)-spaces. As one of the main results, for compact, geodesically complete, 2-dimensional CAT(1)-spaces, we obtain the optimal volume condition to ensure being homeomorphic to the 2-sphere.

Milestones

Received: 7 February 2001

Revised: 20 July 2001

Published: 1 October 2002