# American Institute of Mathematical Sciences

2014, 21: 120-125. doi: 10.3934/era.2014.21.120

## Number of extremal subsets in Alexandrov spaces and rigidity

 1 St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg

Received  April 2014 Published  July 2014

In this paper we announce the following result. 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 $\mathbb{R}^n$ by an action of a crystallographic group. We describe all such actions. We start with a history, results and open questions concerning estimates on the number of extremal subsets in Alexandrov spaces. Then we give the plan of the proof of our result; the complete proof will published elsewhere.
Citation: Nina Lebedeva. Number of extremal subsets in Alexandrov spaces and rigidity. Electronic Research Announcements, 2014, 21: 120-125. doi: 10.3934/era.2014.21.120
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