#### Volume 19, issue 3 (2015)

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Alexandrov spaces with maximal number of extremal points

### Nina Lebedeva

Geometry & Topology 19 (2015) 1493–1521
##### Abstract

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 ${ℝ}^{n}$ by an action of a crystallographic group. We describe all such actions.

##### Keywords
Alexandrov spaces, extremal subsets, orbifolds
##### Mathematical Subject Classification 2010
Primary: 53C45, 53C45, 20F55
Secondary: 51K10
##### Publication
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
##### Authors
 Nina Lebedeva St. Petersburg Department of V A Steklov Institute of Mathematics of RAS Fontanka 27 St. Petersburg 191023 Russia Mathematics Department St. Petersburg State University Universitetsky pr., 28 Stary Peterhof 198504 Russia