Continuity of the volume of simplices in classical geometry

Feng Luo

doi:10.1142/S0219199706002179

Continuity of the volume of simplices in classical geometry

Feng Luo

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

It is proved that the volume of spherical or hyperbolic simplices, when considered as a function of the dihedral angles, can be extended continuously to degenerated simplices. This verifies affirmatively a conjecture of John Minor.

Original language	English (US)
Pages (from-to)	411-431
Number of pages	21
Journal	Communications in Contemporary Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.1142/S0219199706002179
State	Published - Jun 2006

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Hyperbolic space
Simplex
Spherical space
Volume

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10.1142/S0219199706002179

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abstract = "It is proved that the volume of spherical or hyperbolic simplices, when considered as a function of the dihedral angles, can be extended continuously to degenerated simplices. This verifies affirmatively a conjecture of John Minor.",

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KW - Spherical space

KW - Volume

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Continuity of the volume of simplices in classical geometry

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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