Collapsing three-manifolds with a lower curvature bound
type: Item
instance of: scholarly article
title: Collapsing three-manifolds with a lower curvature bound
zbMATH Open document ID: 1252.53051
author: Takashi Shioya
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2012-03-21T00:00:00Z
review text: The author gives a thorough survey on the topic of collapsing 3-manifolds. He gives a proof of a ``volume collapsing theorem'' in an ealier paper [\textit{T. Shioya} and \textit{T. Yamaguchi}, Math. Ann. 333, No. 1, 131--155 (2005; Zbl 1087.53033)]. In this comprehensive paper, the author describes the history of the theorem and the core of the related ideas. He also refers to further papers published later on being based on the same or on different ideas. The author presents the whole story and explains the kernel of the matter, i.e., the so-called ``critical point rescaling argument'' which had already been published earlier in 2000 [\textit{T. Shioya} and \textit{T. Yamaguchi}, J. Differ. Geom. 56, No. 1, 1--66 (2000; Zbl 1036.53028)].
reviewed by: Johann Lang
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 6016703
zbMATH Keywords: Alexandrov spaces
zbMATH Keywords: volume collapsing theorem
zbMATH Keywords: geometrization conjecture
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1325886277
OpenAlex ID: W2022487586
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DOI: 10.2748/TMJ/1325886277
description: scientific article; zbMATH DE number 6016703