alexandrov spaces 1curvature bounded below 1globalization theorem 1gradient flows 1metric geometry 1splitting theorem 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.DG2026
Lectures on Alexandrov spaces with curvature bounded below
Vitali Kapovitch, Nina Lebedeva, Anton Petrunin
This work is an introductory exposition on Alexandrov spaces with curvature bounded below, covering comparison conditions, the globalization theorem, tangent spaces, gradient flows…
math.DG2026
An invitation to Alexandrov geometry: CAT(0) spaces
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
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…
math.DG2025
Alexandrov meets Kirszbraun
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
We give a simplified proof of the generalized Kirszbraun theorem for Alexandrov spaces, which is due to Lang and Schroeder. We also discuss related questions, both solved and open.