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Filling Lipschitz spheres in metric spaces
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.
Related
- Isometric copies of ℓ∞n in Lipschitz-free spaces over finite metric spaces
- Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas
- Characterization of sets in metric spaces where the big Lipschitz derivative is infinite
- Lipschitz numbers and fine differentiability on metric measure spaces
- Lipschitz-free spaces and purely 1-unrectifiable metric spaces
BibTeX
@misc{vikman2026filling,
title = {{Filling Lipschitz spheres in metric spaces}},
author = {Noa Vikman and Stefan Wenger},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05513},
eprint = {2611.05513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05513},
}
RIS
TY - UNPB
TI - Filling Lipschitz spheres in metric spaces
AU - Noa Vikman
AU - Stefan Wenger
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05513
UR - https://arxiv.org/abs/2611.05513
AB - 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.
ER -