11 citations · 54 across the 20 of their papers we have counts for
10 papers · 1 filter
Alexandrov Regions
Nina Lebedeva, Artem Nepechiy
We introduce the notion of Alexandrov region. In contrast to Alexandrov spaces these are intrinsic metric spaces, which satisfy a lower curvature bound and have finite Hausdorff di…
Metric foundations of geometry
Nina Lebedeva, Anton Petrunin
A metric space is called all-set-homogeneous if every isometry between two of its subsets extends to an isometry of the whole space. We classify all-set-homogeneous geodesic spaces…
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…
5-point CAT(0) spaces after Tetsu Toyoda
Nina Lebedeva, Anton Petrunin
We give another proof of Toyoda's theorem that describes 5-point subpaces in CAT(0) length spaces