Volumes of balls in large Riemannian manifolds

Details Volumes of balls in large Riemannian manifolds Volumes of balls in large Riemannian manifolds

2006-10-06

arxiv.org/abs/math/0610212v1

Mathematics

Differential Geometry

21 pages, 1 figure

Scientific paper

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.

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