The central set and its application to the Kneser-Poulsen conjecture
Metric Geometry
2018-02-06 v3 Differential Geometry
Abstract
The Kneser-Poulsen conjecture says that if a finite collection of balls in a Euclidean (spherical or hyperbolic) space is rearranged so that the distance between each pair of centers does not increase, then the volume of the union of these balls does not increase as well. We give new results about central sets of subsets of a Riemannian manifold and apply these results to prove new special cases of the Kneser-Poulsen conjecture in the two-dimensional sphere and the hyperbolic plane.
Keywords
Cite
@article{arxiv.1511.08134,
title = {The central set and its application to the Kneser-Poulsen conjecture},
author = {Igors Gorbovickis},
journal= {arXiv preprint arXiv:1511.08134},
year = {2018}
}
Comments
21 pages, 1 figure