A short proof of Gromov's filling inequality

Stefan Wenger
2008 Proceedings of the American Mathematical Society  
We give a very short and rather elementary proof of Gromov's filling volume inequality for n-dimensional Lipschitz cycles (with integer and Z 2 -coefficients) in L ∞ -spaces. This inequality is used in the proof of Gromov's systolic inequality for closed aspherical Riemannian manifolds and is often regarded as the difficult step therein.
doi:10.1090/s0002-9939-08-09203-4 fatcat:cmatwwd2dvcwzehjcr6tnhqes4