alexandrov spaces 1curvature bounded below 1globalization theorem 1gradient flows 1metric geometry 1splitting theorem 1
From the 1 of 4 linked papers with an AI index.
4 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.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.MG2025
Trees meet octahedron comparison
Nina Lebedeva, Anton Petrunin
We show that trees and their products meet octahedron comparison.
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.