works on
alexandrov spaces 1curvature bounded below 1globalization theorem 1gradient flows 1metric geometry 1splitting theorem 1

From the 1 of 9 linked papers with an AI index.

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20242026
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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.DG2025

Quadratic metric comparisons

Nina Lebedeva, Anton Petrunin, Vladimir Zolotov

We study the effects on length spaces imposed by quadratic inequalities on the six distances between the points in every quadruple.

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.

math.DG2024

Curvature tensor of smoothable Alexandrov spaces

Nina Lebedeva, Anton Petrunin

We prove weak convergence of curvature tensors of Riemannian manifolds for converging noncollapsing sequences with a lower bound on sectional curvature.