Complete noncompact Alexandrov spaces of nonnegative curvature
type: Item
instance of: scholarly article
title: Complete noncompact Alexandrov spaces of nonnegative curvature
zbMATH Open document ID: 0811.53066
DOI: 10.1007/BF01198813
author: Katsuhiro Shiohama
published in: Archiv der Mathematik
publication date: 1993-11-17T00:00:00Z
review text: Let \(X\) be a complete noncompact length metric space, which outside a compact set is locally an \(n\)-dimensional Alexandrov space of nonnegative curvature. The main theorem of this paper is that \(X\) has unbounded \(n\)- dimensional Hausdorff volume. It might have been helpful to point out that the proof depends on a slight generalization of the Burago-Gromov- Perelman-Toponogov comparison theorem, so as to omit a compact set. The end structure of nonnegatively curved Alexandrov spaces is also discussed.
Mathematics Subject Classification ID: 53C70
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C45
zbMATH DE Number: 446327
zbMATH Keywords: Alexandrov space
zbMATH Keywords: nonnegative curvature
zbMATH Keywords: Hausdorff volume
zbMATH Keywords: comparison theorem
zbMATH Keywords: end structure
reviewed by: Stephanie B. Alexander
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 446327