A sphere theorem for 2-dimensional CAT(1)-spaces.
type: Item
instance of: scholarly article
title: A sphere theorem for 2-dimensional CAT(1)-spaces.
zbMATH Open document ID: 1054.53064
author: Koichi Nagano
published in: Pacific Journal of Mathematics
publication date: 2003-02-13T00:00:00Z
review text: Then main result of the paper is the following Theorem: Let \(X\) be a compact, geodesically complete CAT(1)-space whose 2-dimensional Hausdorff measure is at most 3/2 of that of the unit sphere \(S^2\), and the Hausdorff dimension of every sufficiently small neighborhood of every point in \(X\) equals 2. Then either \(X\) is homeomorphic to \(S^2\), or \(X\) is isometric to the 2-polyhedron which is the union of \(S^2\) and the half-sphere \(HS^2\) along the equator. The proof is based on previous results of the author on the volume convergence for Alexandrov spaces of curvature bounded above.
reviewed by: Sergei V. Buyalo
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 53C24
zbMATH DE Number: 1868192
zbMATH Keywords: sphere theorem
zbMATH Keywords: CAT(\(\kappa\))-spaces
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: volume comparison
MaRDI profile type: Publication
full work available at URL: pjm.2002.206.401
OpenAlex ID: W2033471699
DOI: 10.2140/PJM.2002.206.401
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description: scientific article; zbMATH DE number 1868192