PreprintarXiv licencearXiv
CAT(0) spaces without linear filling at the asymptotic rank
Abstract
For every integer ν≥ 2, we construct a (ν+1)-dimensional, locally compact, geodesically complete CAT(0) space of asymptotic rank ν which does not satisfy a linear isoperimetric inequality for integral ν-cycles. Its filling function is bounded below by c vlog v for all sufficiently large v.
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BibTeX
@misc{stadler2026cat0,
title = {{CAT(0) spaces without linear filling at the asymptotic rank}},
author = {Stephan Stadler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33633},
eprint = {2609.33633},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33633},
}
RIS
TY - UNPB
TI - CAT(0) spaces without linear filling at the asymptotic rank
AU - Stephan Stadler
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33633
UR - https://arxiv.org/abs/2609.33633
AB - For every integer ν≥ 2, we construct a (ν+1)-dimensional, locally compact, geodesically complete CAT(0) space of asymptotic rank ν which does not satisfy a linear isoperimetric inequality for integral ν-cycles. Its filling function is bounded below by c vlog v for all sufficiently large v.
ER -