Two-dimensional metric spaces with curvature bounded above I
Metric Geometry
2024-12-04 v3 Differential Geometry
Abstract
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
Cite
@article{arxiv.2102.00623,
title = {Two-dimensional metric spaces with curvature bounded above I},
author = {Koichi Nagano and Takashi Shioya and Takao Yamaguchi},
journal= {arXiv preprint arXiv:2102.00623},
year = {2024}
}
Comments
73 pages, 12figures, Theorem 1.5 was removed, and the proof of Lemma 7.16 was modified