Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone
On existence of PI-exponents of codimension growth
Number of extremal subsets in Alexandrov spaces and rigidity
Nina Lebedeva 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.
Keywords: orbifolds., extremal subsets, Alexandrov spaces.
Mathematics Subject Classification: 51K10, 53C45, 20F5.
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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Nina Lebedeva