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Alexandrov spaces with maximal number of extremal points

Nina Lebedeva

Geometry & Topology 19 (2015) 1493–1521

We show that any n–dimensional nonnegatively curved Alexandrov space with the maximal possible number of extremal points is isometric to a quotient space of n by an action of a crystallographic group. We describe all such actions.

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Alexandrov spaces, extremal subsets, orbifolds
Mathematical Subject Classification 2010
Primary: 53C45, 53C45, 20F55
Secondary: 51K10
Received: 26 December 2013
Revised: 21 May 2014
Accepted: 25 June 2014
Published: 21 May 2015
Proposed: John Lott
Seconded: Tobias H Colding, Dmitri Burago
Nina Lebedeva
St. Petersburg Department of V A Steklov Institute of Mathematics of RAS
Fontanka 27
St. Petersburg
Mathematics Department
St. Petersburg State University
Universitetsky pr., 28
Stary Peterhof