Alexandrov spaces with maximal number of extremal points. (English) Zbl 1318.53074

Summary: 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.


53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
20F55 Reflection and Coxeter groups (group-theoretic aspects)
51K10 Synthetic differential geometry
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