Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Kapovitch Vitali"'
Autor:
Kapovitch Vitali, Lytchak Alexander
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 9, Iss 1, Pp 53-64 (2021)
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.
Externí odkaz:
https://doaj.org/article/3155ae78093a4e5da12006a0eb37260d
Autor:
Kapovitch Vitali, Ketterer Christian
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 7, Iss 1, Pp 197-211 (2019)
We show that if a CD(K, n) space (X, d, f ℋn) with n ≥ 2 has curvature bounded above by κ in the sense of Alexandrov then f is constant.
Externí odkaz:
https://doaj.org/article/7996574547c940ecb3e788bf8b7c15d6
Autor:
Deng, Qin, Kapovitch, Vitali
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 analyze almost rigidity. Our results are new even for smooth manifolds wit
Externí odkaz:
http://arxiv.org/abs/2308.14668
Autor:
Kapovitch, Vitali, Zhu, Xingyu
We show that if an Alexandrov space $X$ has an Alexandrov subspace $\bar \Omega$ of the same dimension disjoint from the boundary of $X$, then the topological boundary of $\bar \Omega$ coincides with its Alexandrov boundary. Similarly, if a noncollap
Externí odkaz:
http://arxiv.org/abs/2210.07405
Autor:
Kapovitch, Vitali, Lytchak, Alexander
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.
Externí odkaz:
http://arxiv.org/abs/2101.03050
Autor:
Kapovitch, Vitali, Lytchak, Alexander
Publikováno v:
Geom. Topol. 26 (2022) 2649-2711
We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.
Externí odkaz:
http://arxiv.org/abs/2007.01325
In this paper we prove that in the class of metric measure spaces with Alexandrov curvature bounded from below the Riemannian curvature-dimension condition $RCD(K,N)$ with $K\in \mathbb{R}$ and $N\in [1,\infty)$ is preserved under doubling and gluing
Externí odkaz:
http://arxiv.org/abs/2003.06242
Autor:
Kapovitch, Vitali
Publikováno v:
Geom. Topol. 25 (2021) 2017-2059
We prove a mixed curvature analogue of Gromov's almost flat manifolds theorem for upper sectional and lower Bakry-Emery Ricci curvature bounds.
Externí odkaz:
http://arxiv.org/abs/1911.09212
We develop a structure theory for RCD spaces with curvature bounded above in Alexandrov sense. In particular, we show that any such space is a topological manifold with boundary whose interior is equal to the set of regular points. Further the set of
Externí odkaz:
http://arxiv.org/abs/1908.07036
Autor:
Kapovitch, Vitali, Mondino, Andrea
Publikováno v:
Geom. Topol. 25 (2021) 445-495
We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties,
Externí odkaz:
http://arxiv.org/abs/1907.02614