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arXiv · 1810.13056

Volume pinching theorems for CAT(1) spaces

Koichi Nagano
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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.

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Koichi Nagano. 2018-10-31. Volume pinching theorems for CAT(1) spaces. https://arxiv.org/abs/1810.13056

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