Collapsing three-manifolds with a lower curvature bound
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)].
scientific article; zbMATH DE number 6016703
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