Volumes of balls in large Riemannian manifolds
Differential Geometry
2007-05-23 v1
Abstract
If (M^n, g) is a complete Riemannian manifold with filling radius at least R, then we prove that it contains a ball of radius R and volume at least c(n)R^n. If (M^n, hyp) is a closed hyperbolic manifold and if g is another metric on M with volume at most c(n)Volume(M,hyp), then we prove that the universal cover of (M,g) contains a unit ball with volume greater than the volume of a unit ball in hyperbolic n-space.
Cite
@article{arxiv.math/0610212,
title = {Volumes of balls in large Riemannian manifolds},
author = {Larry Guth},
journal= {arXiv preprint arXiv:math/0610212},
year = {2007}
}
Comments
21 pages, 1 figure