Volume pinching theorems for CAT(1) spaces

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.

A final version, modified the texts in Section 4

References in corpus (1)

• Topological regularity of spaces with an upper curvature bound

Cited by in corpus (2)

• Discrete groups of packed, non-positively curved, Gromov hyperbolic metric spaces
• Noncritical maps on geodesically complete spaces with curvature bounded above