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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



A panoramic glimpse of manifolds with sectional curvature bounded from below

Author: K. Grove
Original publication: Algebra i Analiz, tom 29 (2017), nomer 1.
Journal: St. Petersburg Math. J. 29 (2018), 3-31
MSC (2010): Primary 53C20, 53C23, 57S15
Published electronically: December 27, 2017
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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.

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Additional Information

K. Grove
Affiliation: University of Notre Dame 255 Hurley South Bend, IN 46556 USA

Keywords: Lower curvature bound, Toponogov distance comparison theorem, Bishop--Gromov volume comparison theorem, Gromov--Hausdorff topology, metric critical point theory
Received by editor(s): September 6, 2016
Published electronically: December 27, 2017
Additional Notes: Supported in part by a grant from the National Science Foundation
Dedicated: Dedicated to Yu. D. Burago on his 80th birthday
Article copyright: © Copyright 2017 American Mathematical Society

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