TY - JOUR

T1 - Upper Bounds for Volumes of Generalized Hyperbolic Polyhedra and Hyperbolic Links

AU - Vesnin, A. Yu

AU - Egorov, A. A.

N1 - The research was supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS” and the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0004)

PY - 2024/5

Y1 - 2024/5

N2 - Call a polyhedron in a three-dimensional hyperbolic spacegeneralized if finite, ideal, and truncated vertices are admitted.By Belletti’s theorem of 2021 the exact upper bound for the volumesof generalized hyperbolic polyhedra with the same one-dimensional skeleton equals the volume of an ideal right-angled hyperbolic polyhedronwhose one-dimensional skeleton is the medial graph for.We give the upper bounds for the volume ofan arbitrary generalized hyperbolic polyhedronsuch that the bounds depend linearly onthe number of edges. Moreover, we show that the bounds can be improvedif the polyhedron has triangular faces and trivalent vertices.As application we obtain some new upper bounds for the volumeof the complement of the hyperbolic link with more than eight twists in a diagram.

AB - Call a polyhedron in a three-dimensional hyperbolic spacegeneralized if finite, ideal, and truncated vertices are admitted.By Belletti’s theorem of 2021 the exact upper bound for the volumesof generalized hyperbolic polyhedra with the same one-dimensional skeleton equals the volume of an ideal right-angled hyperbolic polyhedronwhose one-dimensional skeleton is the medial graph for.We give the upper bounds for the volume ofan arbitrary generalized hyperbolic polyhedronsuch that the bounds depend linearly onthe number of edges. Moreover, we show that the bounds can be improvedif the polyhedron has triangular faces and trivalent vertices.As application we obtain some new upper bounds for the volumeof the complement of the hyperbolic link with more than eight twists in a diagram.

KW - 514.132:515.162

KW - Lobachevsky geometry hyperbolic space

KW - augmented links

KW - hyperbolic knots and links

KW - volumes of hyperbolic polyhedra

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85195133256&origin=inward&txGid=924a8aeab3ed43a3760739e839daf851

UR - https://www.mendeley.com/catalogue/bc3c8505-2fa3-3443-938e-c316f94ea7e3/

U2 - 10.1134/S0037446624030042

DO - 10.1134/S0037446624030042

M3 - Article

VL - 65

SP - 534

EP - 551

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -