Geodesic
Volumes of balls in large Riemannian manifolds
Larry Guth1
1 Department of Mathematics<br/>University of Toronto<br/>Toronto Ontario<br/> Canada M5S 2E4
Annals of mathematics, Tome 173 (2011) no. 1, pp. 51-76.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $(M^n, \mathrm{hyp})$ is a closed hyperbolic manifold and if $g$ is another metric on $M$ with volume no greater than $\delta(n) \mathrm{Vol}(M, \mathrm{hyp})$, 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.
DOI : 10.4007/annals.2011.173.1.2

Larry Guth 1

1 Department of Mathematics<br/>University of Toronto<br/>Toronto Ontario<br/> Canada M5S 2E4 
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Larry Guth. Volumes of balls in large Riemannian manifolds. Annals of mathematics, Tome 173 (2011) no. 1, pp. 51-76. doi : 10.4007/annals.2011.173.1.2. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.1.2/

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