An invitation to Alexandrov geometry: CAT(0) spaces
Differential Geometry
2026-01-16 v4 Algebraic Topology
Metric Geometry
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.
Cite
@article{arxiv.1701.03483,
title = {An invitation to Alexandrov geometry: CAT(0) spaces},
author = {Stephanie Alexander and Vitali Kapovitch and Anton Petrunin},
journal= {arXiv preprint arXiv:1701.03483},
year = {2026}
}
Comments
Draft of the 2nd edition