141 citations · 555 across the 57 of their papers we have counts for
13 papers · 1 filter
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…
An isoperimetric inequality for mean shadow
Roman Karasev, Anton Petrunin, Alexander Plakhov
We prove an isoperimetric inequality in terms of the mean shadow area.
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…
Weak topology on CAT(0) spaces
Alexander Lytchak, Anton Petrunin
We analyze weak convergence on CAT(0) spaces and the existence and properties of corresponding weak topologies.