141 citations · 555 across the 57 of their papers we have counts for
4 papers · 2 filters
Curvature bounded below: a definition a la Berg--Nikolaev
Nina Lebedeva, Anton Petrunin
We give a new characterization of spaces with nonnegative curvature in the sense of Alexandrov.
Uniquely constructed figures
Anton Petrunin, Serge Rukshin
A convex figures F is called uniquely constructed if it satisfies the following condition: if F equidecomposable to a convex figure G then F is congruent to G. We classify all conv…
Alexandrov meets Lott--Villani--Sturm
Anton Petrunin
Here I show compatibility of two definition of generalized curvature bounds --- the lower bound for sectional curvature in the sense of Alexandrov and lower bound for Ricci curvatu…
Intrinsic isometries in Euclidean space
Anton Petrunin
I consider compact metric spaces which admit intrinsic isometries to Euclidean d-space. The main result roughly states that the class of these spaces coincides with class of invers…