no code implementations • 8 Jan 2021 • Vitali Kapovitch, Alexander Lytchak
We discuss folklore statements about distance functions in manifolds with two sided bounded curvature.
Differential Geometry Metric Geometry 53C20, 53C21, 53C23
1 code implementation • 20 Mar 2019 • Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
This book includes material up to the definition of dimension.
Differential Geometry Metric Geometry 53C23, 53C45, 30L99
1 code implementation • 24 Jul 2017 • Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann
We present a condition for towers of fiber bundles which implies that the fundamental group of the total space has a nilpotent subgroup of finite index whose torsion is contained in its center.
Algebraic Topology Differential Geometry 57R19, 55R10, 53C20
1 code implementation • 12 May 2017 • Vitali Kapovitch, Alexander Lytchak, Anton Petrunin
We relate the existence of many infinite geodesics on Alexandrov spaces to a statement about the average growth of volumes of balls.
Differential Geometry Metric Geometry 53C20, 52A15, 53C23
1 code implementation • 12 Jan 2017 • Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
The idea is to demonstrate the beauty and power of Alexandrov geometry by reaching interesting applications with a minimum of preparation.
Differential Geometry Algebraic Topology Metric Geometry 53-01, 53C23, 53C45
1 code implementation • 27 Dec 2010 • Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
We give a simplified proof of the generalized Kirszbraun theorem for Alexandrov spaces, which is due to Lang and Schroeder.
Differential Geometry 53C23 53C45
1 code implementation • 14 Jun 2005 • Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann
We show that almost nonnegatively curved m-dimensional manifolds are, up to finite cover, nilpotent spaces in the sense of homotopy theory and have C(m)-nilpotent fundamental groups.
Differential Geometry 53C20
