141 citations · 555 across the 57 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…
Polyhedral approximations of Riemannian manifolds
Anton Petrunin
We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above. We show that th…
Six proofs of the Fáry--Milnor theorem
Anton Petrunin, Stephan Stadler
We sketch several proofs of Fáry--Milnor theorem.