We prove that if a finitely presented group actsproperly discontinuously, cocompactly and by isometries on asimply connected Riemannian manifold, then the Dehn function ofthe group and the corresponding filling function of the manifoldare equivalent, in a sense described below. We also prove thisresult for simplicial complexes X where the metric on Xrestricts to a Riemannian metric with corners on each simplex.
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