Upper Bounds for Volumes of Generalized Hyperbolic Polyhedra and Hyperbolic Links Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
||||
|---|---|---|---|---|---|
| Output data | Year: 2024, Volume: 65, Number: 3, Pages: 534 - 551 Pages count : 18 DOI: 10.1134/S0037446624030042 | ||||
| Tags | Lobachevsky geometry hyperbolic space, volumes of hyperbolic polyhedra, hyperbolic knots and links, augmented links | ||||
| Authors |
|
||||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
Call a polyhedron in a three-dimensional hyperbolic space generalized if finite, ideal, and truncated vertices are admitted. By Belletti’s theorem of 2021 the exact upper bound for the volumes of generalized hyperbolic polyhedra with the same one-dimensional skeleton Γ equals the volume of an ideal right-angled hyperbolic polyhedron whose one-dimensional skeleton is the medial graph for Γ. We give the upper bounds for the volume of an arbitrary generalized hyperbolic polyhedron such that the bounds depend linearly on the number of edges. Moreover, we show that the bounds can be improved if the polyhedron has triangular faces and trivalent vertices. As application we obtain some new upper bounds for the volume of the complement of the hyperbolic link with more than eight twists in a diagram.
Cite:
Vesnin A.Y.
, Egorov A.A.
Upper Bounds for Volumes of Generalized Hyperbolic Polyhedra and Hyperbolic Links
Siberian Mathematical Journal. 2024. V.65. N3. P.534 - 551. DOI: 10.1134/S0037446624030042 WOS Scopus РИНЦ OpenAlex
Upper Bounds for Volumes of Generalized Hyperbolic Polyhedra and Hyperbolic Links
Siberian Mathematical Journal. 2024. V.65. N3. P.534 - 551. DOI: 10.1134/S0037446624030042 WOS Scopus РИНЦ OpenAlex
Original:
Веснин А.Ю.
, Егоров А.А.
Верхние оценки объемов гиперболических многогранников и зацеплений
Сибирский математический журнал. 2024. Т.65. №3. С.469-488. DOI: 10.33048/smzh.2024.65.304 РИНЦ
Верхние оценки объемов гиперболических многогранников и зацеплений
Сибирский математический журнал. 2024. Т.65. №3. С.469-488. DOI: 10.33048/smzh.2024.65.304 РИНЦ
Dates:
| Submitted: | Jul 18, 2023 |
| Accepted: | Feb 26, 2024 |
| Published print: | May 29, 2024 |
| Published online: | May 29, 2024 |
Identifiers:
| Web of science: | WOS:001235366000021 |
| Scopus: | 2-s2.0-85195133256 |
| Elibrary: | 67311441 |
| OpenAlex: | W4399125228 |
Citing:
Пока нет цитирований