Alexandrov spaces with maximal number of extremal points

TL;DR

This paper characterizes n-dimensional nonnegatively curved Alexandrov spaces with the maximum number of extremal points, showing they are quotients of Euclidean space by crystallographic groups, and describes all such group actions.

Contribution

It provides a complete classification of extremal point-maximal Alexandrov spaces as quotients of Euclidean space by crystallographic groups, including all such group actions.

Findings

Spaces with maximal extremal points are quotients of Euclidean space.

All such quotient spaces are characterized by crystallographic group actions.

The paper describes all possible crystallographic group actions leading to these spaces.

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 Euclidean n -space by an action of a crystallographic group. We describe all such actions.