Alexandrov spaces with maximal number of extremal points

Lebedeva, Nina

doi:10.2140/gt.2015.19.1493

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Alexandrov spaces with maximal number of extremal points

Nina Lebedeva

Geometry & Topology 19 (2015) 1493–1521

DOI: 10.2140/gt.2015.19.1493

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

References

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

Volume 19, issue 3 (2015)