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Two-dimensional metric
spaces with curvature bounded above, I
Koichi Nagano, Takashi Shioya and Takao Yamaguchi |
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Geometry & Topology 28 (2024) 3023–3093
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Abstract |
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We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the topological singular point set of such a singular surface. |
Keywords
upper curvature bound, ruled surface, singular set
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Mathematical Subject Classification
Primary: 53C20, 53C23
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References |
Publication
Received: 5 February 2021
Revised: 28 August 2022
Accepted: 13 July 2023
Published: 25 November 2024
Proposed: Bruce Kleiner
Seconded: John Lott, Tobias H Colding
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Authors |
| Koichi Nagano | |
| Department of Mathematics University of Tsukuba Tsukuba Japan |
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| Takashi Shioya | |
| Mathematical Institute Tohoku University Sendai Japan |
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| Takao Yamaguchi | |
| Department of Mathematics Kyoto University Kyoto Japan |
Department of Mathematics University of Tsukuba Tsukuba Japan |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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