New definitions of Alexandrov space and applications
Differential Geometry
2023-08-30 v2 Metric Geometry
Abstract
In this paper we show that, in the definition of Alexandrov spaces with lower or upper curvature bound, the original conditions can be replaced with much weaker ones. For the purpose, we introduce `imaginary' comparison angles (and `imaginary' angles), and the right or left bounded second derivative in the support sense. As applications, we provide new proofs for the Doubling Theorem, and the Globalization Theorem for complete or geodesic Alexandrov spaces with lower curvature bound.
Keywords
Cite
@article{arxiv.2102.02112,
title = {New definitions of Alexandrov space and applications},
author = {Shengqi Hu and Xiaole Su and Yusheng Wang},
journal= {arXiv preprint arXiv:2102.02112},
year = {2023}
}
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24 pages