52 citations · 281 across the 29 of their papers we have counts for
35 papers
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,…
Sharp bounds and rigidity for volumes of boundaries of Alexandrov spaces
Qin Deng, Vitali Kapovitch
We obtain sharp volume bounds on the boundaries of Alexandrov spaces with given lower curvature bound, dimension, and radius. We also completely classify the rigidity case and anal…
On the intrinsic and extrinsic boundary for metric measure spaces with lower curvature bounds
Vitali Kapovitch, Xingyu Zhu
We show that if an Alexandrov space has an Alexandrov subspace of the same dimension disjoint from the boundary of , then the topological boundary of coinc…
Remarks on manifolds with two sided curvature bounds
Vitali Kapovitch, Alexander Lytchak
We discuss folklore statements about distance functions in manifolds with two sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.
Structure of Submetries
Vitali Kapovitch, Alexander Lytchak
We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.
On gluing Alexandrov spaces with lower Ricci curvature bounds
Vitali Kapovitch, Christian Ketterer, Karl-Theodor Sturm
In this paper we prove that in the class of metric measure spaces with Alexandrov curvature bounded from below the Riemannian curvature-dimension condition with $K\in \m…