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arXiv · 2308.14668

Sharp bounds and rigidity for volumes of boundaries of Alexandrov spaces

Qin Deng·Vitali Kapovitch
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Abstract

We obtain sharp volume bounds on the boundaries of Alexandrov spaces with given lower curvature bound, dimension, and radius. We also completely classify the rigidity case and analyze almost rigidity. Our results are new even for smooth manifolds with boundary.

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Qin Deng, Vitali Kapovitch. 2023-08-28. Sharp bounds and rigidity for volumes of boundaries of Alexandrov spaces. https://arxiv.org/abs/2308.14668

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