A short proof of Gromov's filling inequality

Abstract

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 $L^{\infty }$-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.

4 pages

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