PreprintarXiv licencearXiv
Dimension bounds for finite-volume hyperbolic Coxeter polytopes
Abstract
We prove that a finite-volume hyperbolic Coxeter polytope has dimension at most $81$, substantially improving Prokhorov's bound of $995$. A refinement of Prokhorov's method gives the intermediate bound $162$, while an extension of Vinberg's planar-angle comparison to the finite-volume setting yields the sharper bound. Both arguments combine improved weighting functions with estimates using cusp geometry to control weight contributions of angles at ideal vertices or edges incident to them.
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BibTeX
@misc{guo2026dimension,
title = {{Dimension bounds for finite-volume hyperbolic Coxeter polytopes}},
author = {Lizi Guo and Fangting Zheng},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01795},
eprint = {2611.01795},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01795},
}
RIS
TY - UNPB
TI - Dimension bounds for finite-volume hyperbolic Coxeter polytopes
AU - Lizi Guo
AU - Fangting Zheng
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01795
UR - https://arxiv.org/abs/2611.01795
AB - We prove that a finite-volume hyperbolic Coxeter polytope has dimension at most $81$, substantially improving Prokhorov's bound of $995$. A refinement of Prokhorov's method gives the intermediate bound $162$, while an extension of Vinberg's planar-angle comparison to the finite-volume setting yields the sharper bound. Both arguments combine improved weighting functions with estimates using cusp geometry to control weight contributions of angles at ideal vertices or edges incident to them.
ER -