Two-dimensional metric spaces with curvature bounded above II

2023/08/31 by Nagano, Koichi, Shioya, Takashi, Yamaguchi, Takao
#53C20 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2308.16398

Abstract

As a continuation of \citeNSY:local, we mainly discuss the global structure of two-dimensional locally compact geodesically complete metric spaces with curvature bounded above. We first obtain the result on the Lipschitz homotopy approximations of such spaces by polyhedral spaces. We define the curvature measures on our spaces making use of the convergence of the curvature measures, and establish Gauss-Bonnet Theorem. We also give a characterization of such spaces.

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