Volume of a doubly truncated hyperbolic tetrahedron

Alexander Kolpakov; Jun Murakami

doi:10.1007/s00010-012-0153-y

Volume of a doubly truncated hyperbolic tetrahedron

Alexander Kolpakov, Jun Murakami

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the earlier results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.

Original language	English
Pages (from-to)	449-463
Number of pages	15
Journal	Aequationes Mathematicae
Volume	85
Issue number	3
DOIs	https://doi.org/10.1007/s00010-012-0153-y
Publication status	Published - 2013 Jun

Keywords

Gram matrix
Hyperbolic tetrahedron
volume formula

ASJC Scopus subject areas

Mathematics(all)
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1007/s00010-012-0153-y

Fingerprint Dive into the research topics of 'Volume of a doubly truncated hyperbolic tetrahedron'. Together they form a unique fingerprint.

Cite this

Kolpakov, A., & Murakami, J. (2013). Volume of a doubly truncated hyperbolic tetrahedron. Aequationes Mathematicae, 85(3), 449-463. https://doi.org/10.1007/s00010-012-0153-y

@article{62d0c1d36e8a4997856490643b128c77,

title = "Volume of a doubly truncated hyperbolic tetrahedron",

abstract = "The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the earlier results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.",

keywords = "Gram matrix, Hyperbolic tetrahedron, volume formula",

author = "Alexander Kolpakov and Jun Murakami",

year = "2013",

month = jun,

doi = "10.1007/s00010-012-0153-y",

language = "English",

volume = "85",

pages = "449--463",

journal = "Aequationes Mathematicae",

issn = "0001-9054",

publisher = "Birkhauser Verlag Basel",

number = "3",

}

TY - JOUR

T1 - Volume of a doubly truncated hyperbolic tetrahedron

AU - Kolpakov, Alexander

AU - Murakami, Jun

PY - 2013/6

Y1 - 2013/6

N2 - The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the earlier results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.

AB - The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the earlier results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.

KW - Gram matrix

KW - Hyperbolic tetrahedron

KW - volume formula

UR - http://www.scopus.com/inward/record.url?scp=84878871399&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878871399&partnerID=8YFLogxK

U2 - 10.1007/s00010-012-0153-y

DO - 10.1007/s00010-012-0153-y

M3 - Article

AN - SCOPUS:84878871399

VL - 85

SP - 449

EP - 463

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

SN - 0001-9054

IS - 3

ER -