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arXiv · 1701.03483

An invitation to Alexandrov geometry: CAT(0) spaces

Stephanie Alexander·Vitali Kapovitch·Anton Petrunin
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Abstract

Our goal is to show the beauty and power of Alexandrov geometry by reaching interesting applications and theorems with a minimum of preparation. The topics include 1. Reshetnyak's gluing theorem, 2. Estimates on the number of collisions in billiards, 3. Reshetnyak's majorization theorem, 4. Hadamard--Cartan globalization theorem, 5. Polyhedral spaces, 6. Construction of exotic aspherical manifolds, 7. The geometry of two-convex sets in Euclidean space, 8. Barycenters and dimension theory.

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Stephanie Alexander, Vitali Kapovitch, Anton Petrunin. 2017-01-12. An invitation to Alexandrov geometry: CAT(0) spaces. https://arxiv.org/abs/1701.03483

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