arXiv:2611.05513v1 Announce Type: new Abstract: We prove a homotopical Euclidean isoperimetric inequality for Lipschitz maps from the unit n-sphere into metric spaces admitting a bounded bicombing, which includes CAT(0)-spaces and normed vector spaces. To do so, we first refine the second-named author's Euclidean isoperimetric inequality for singular Lipschitz chains to this setting. Then, we show that a singular Lipschitz chain filling induces a Lipschitz map filling of almost the same volume or less, by adapting a strategy seen in work of Gromov and others.
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