PreprintarXiv licencearXiv
Sharp dimension bounds for right-angled hyperbolic polytopes
Abstract
We determine the largest dimensions in which right-angled hyperbolic polytopes of finite volume can exist. The dimension is at most eight in general, and at most four when all vertices lie at infinity. Both bounds are attained, improving the previously known upper bounds of twelve and six. Our proofs use elementary properties of hyperbolic polytopes together with bounds for configurations of points on spheres.
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BibTeX
@misc{kolpakov2026sharp,
title = {{Sharp dimension bounds for right-angled hyperbolic polytopes}},
author = {Alexander Kolpakov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38900},
eprint = {2610.38900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38900},
}
RIS
TY - UNPB
TI - Sharp dimension bounds for right-angled hyperbolic polytopes
AU - Alexander Kolpakov
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38900
UR - https://arxiv.org/abs/2610.38900
AB - We determine the largest dimensions in which right-angled hyperbolic polytopes of finite volume can exist. The dimension is at most eight in general, and at most four when all vertices lie at infinity. Both bounds are attained, improving the previously known upper bounds of twelve and six. Our proofs use elementary properties of hyperbolic polytopes together with bounds for configurations of points on spheres.
ER -