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 › peer-review

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

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10.1007/s00010-012-0153-y

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author = "Alexander Kolpakov and Jun Murakami",

note = "Funding Information: A. Kolpakov was supported by the Schweizerischer National fonds SNF no. 200021-131967/1. J. Murakami was supported by Grant-in-Aid for Scientific Research no. 22540236.",

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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.

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KW - Hyperbolic tetrahedron

KW - volume formula

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