11 citations · 54 across the 20 of their papers we have counts for
22 papers
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…
Lectures on Alexandrov spaces with curvature bounded below
Vitali Kapovitch, Nina Lebedeva, Anton Petrunin
An introduction to Alexandrov spaces with curvature bounded below. Topics include various comparison conditions, the globalization theorem, tangent spaces and spaces of directions,…
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.
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…