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Volume pinching theorems for CAT(1) spaces
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 144, Number 1, February 2022
- pp. 267-285
- 10.1353/ajm.2022.0005
- Article
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Abstract:
We examine volume pinching problems of ${\rm CAT}(1)$ spaces. We characterize a class of compact geodesically complete ${\rm CAT}(1)$ spaces of small specific volume. We prove a sphere theorem for compact ${\rm CAT}(1)$ homology manifolds of small volume. We also formulate a criterion of manifold recognition for homology manifolds on volume growths under an upper curvature bound.