Volumes of balls in large Riemannian manifolds

• 成果类型: Article
• 署名作者: Guth, Larry
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.1.2
• 发表日期: 2011
• 页码: 51-76
• 关键词: curvature

摘要

We prove two lower bounds for the volumes of balls in a Riemannian manifold. If (M-n, g) is a complete Riemannian manifold with filling radius at least R, then it contains a ball of radius R and volume at least delta(n)R-n If (M-n, hyp) is a closed hyperbolic manifold and if g is another metric on M with volume no greater than delta(n)Vol(M, hyp), then the universal cover of (M, g) contains a unit ball with volume greater than the volume of a unit ball in hyperbolic n-space.