TY - JOUR

T1 - Volume Estimates for Right-Angled Hyperbolic Polyhedra

AU - Egorov, Andrey

AU - Vesnin, Andrei

N1 - Funding Information: The work was supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS”. Funding Information: The work was supported by the Theoretical Physics and Mathematics Advance-ment Foundation ?BASIS?. Publisher Copyright: © 2020. All Rights Reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - By Andreev theorem acute-angled polyhedra of finite vo-lume in a hyperbolic space (Formula presented)3are uniquely determined by combinatorics of their 1-skeletons and dihedral angles. For a class of compact right-angled polyhedra and a class of ideal right-angled polyhedra estimates of volumes in terms of the number of vertices were obtained by Atkin-son in 2009. In the present paper upper estimates for both classes are improved.

AB - By Andreev theorem acute-angled polyhedra of finite vo-lume in a hyperbolic space (Formula presented)3are uniquely determined by combinatorics of their 1-skeletons and dihedral angles. For a class of compact right-angled polyhedra and a class of ideal right-angled polyhedra estimates of volumes in terms of the number of vertices were obtained by Atkin-son in 2009. In the present paper upper estimates for both classes are improved.

KW - hyperbolic volume

KW - ideal polyhedron

KW - right-angled polyhedron

UR - http://www.scopus.com/inward/record.url?scp=85108694417&partnerID=8YFLogxK

U2 - 10.13137/2464-8728/30958

DO - 10.13137/2464-8728/30958

M3 - Article

AN - SCOPUS:85108694417

VL - 52

SP - 565

EP - 576

JO - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

JF - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

SN - 0049-4704

ER -