2012/05/02 by Takao Yamaguchi, Yamaguchi, Takao · 2 citations
Computer Science · Mathematics · #53C20 #53C23 (Primary) #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.DG #msc:53C20 #msc:53C23
paper · pdf · doi:10.48550/arxiv.1205.0441
arxiv created 2012/05/02 · openalex publication_date 2012/05/02 · arxiv updated 2012/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essential coverings by contractible metric balls, and provide a uniform bound on the numbers of contractible metric balls forming essential coverings of the spaces in the family. In particular, this gives another view for Gromov's Betti number theorem.