A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications
type: Item
instance of: scholarly article
title: A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications
zbMATH Open document ID: 1191.53051
author: Ayato Mitsuishi
published in: Geometriae Dedicata
publication date: 2010-02-25T00:00:00Z
review text: The author proves a splitting theorem for Alexandrov spaces of nonnegative curvature without properness assumptions [c.f., \textit{A. D. Milka}, Ukr. Geom. Sb. 4, 43--48 (1967; Zbl 0184.47404)]: Theorem. Let \(X\) be an Alexandrov space of nonnegative curvature. Then \(X\) is isometric to the direct product of some Hilbert space and some Alexandrov space with nonnegative curvature which contains no lines. As a corollary, a maximal radius theorem for Alexandrov spaces of curvature bounded from below is obtained without properness assumptions: Corollary. If an Alexandrov space \(X\) of curvature \(\geq 1\) has radius equal to \(\pi\), then \(X\) is isometric to the unit sphere of some Hilbert space with angle metric. Finally, new examples of infinite dimensional Alexandrov spaces of nonnegative curvature are found.
reviewed by: Anatoliy Milka
Mathematics Subject Classification ID: 53C45
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 5675138
zbMATH Keywords: Alexandrov space
zbMATH Keywords: curvature
zbMATH Keywords: splitting theorem
zbMATH Keywords: maximal radius sphere theorem
MaRDI profile type: Publication
full work available at URL: s10711-009-9390-1
OpenAlex ID: W1996028370
cites work: A course in metric geometry
cites work: Q4720067
cites work: Convex analysis and measurable multifunctions
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cites work: Q4380377
cites work: Spaces of Wald curvature bounded below
cites work: Nonlinear Markov operators, discrete heat flow, and harmonic maps between singular spaces
DOI: 10.1007/S10711-009-9390-1
description: scientific article; zbMATH DE number 5675138