11 citations · 54 across the 20 of their papers we have counts for
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Alexandrov's embedding theorem
Nina Lebedeva, Anton Petrunin
Written for the book "Mathematicians from Saint Petersburg and their theorems".
Graph comparison meets Alexandrov
Nina Lebedeva, Anton Petrunin
Graph comparison is a certain type of condition on metric space encoded by a finite graph. We show that any nontrivial graph comparison implies one of Alexandrov's comparisons. The…
Trees meet octahedron comparison
Nina Lebedeva, Anton Petrunin
We show that trees and their products meet octahedron comparison.
All-set-homogeneous spaces
Nina Lebedeva, Anton Petrunin
A metric space is said to be all-set-homogeneous if any of its partial isometries can be extended to a genuine isometry. We give a classification of a certain subclass of all-set-h…
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.
Five-point Toponogov theorem
Nina Lebedeva, Anton Petrunin
We give an if-and-only-if condition on a five-point metric spaces that admit embeddings into nonnegatively curved Riemannian manifolds.