Two-dimensional metric spaces with curvature bounded above, I

Nagano, Koichi¹ ; Shioya, Takashi² ; Yamaguchi, Takao³

¹ Department of Mathematics, University of Tsukuba, Tsukuba, Japan
² Mathematical Institute, Tohoku University, Sendai, Japan
³ Department of Mathematics, Kyoto University, Kyoto, Japan, Department of Mathematics, University of Tsukuba, Tsukuba, Japan

Geometry & topology, Tome 28 (2024) no. 7, pp. 3023-3093

Résumé

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.

Détail

DOI : 10.2140/gt.2024.28.3023

Keywords: upper curvature bound, ruled surface, singular set

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