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JOURNALS // Algebra i Analiz // Archive

Algebra i Analiz, 2017 Volume 29, Issue 1, Pages 7–48 (Mi aa1520)

This article is cited in 3 papers

Expository Surveys

A panoramic glimpse of manifolds with sectional curvature bounded from below

K. Grove

University of Notre Dame, 255 Hurley, South Bend, IN 46556, USA

Abstract: Rather than providing a comprehensive survey on manifolds curved from below, the paper is aimed at exhibiting and discussing some of the main ideas and tools that have been developed over decades. For the same reason, only a relatively small sample of results is presented to illustrate this development and in doing this, simplicity is emphasized over generality. In the same vein, at most a glimpse of an idea or strategy of a proof is given.

Keywords: lower curvature bound, Toponogov distance comparison theorem, Bishop–Gromov volume comparison theorem, Gromov–Hausdorff topology.

Received: 06.09.2016

Language: English


 English version:
St. Petersburg Mathematical Journal, 2018, 29:1, 3–31

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