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Simplices of maximal volume or minimal total edge length in hyperbolic space

Peyerimhoff, N.

Authors



Abstract

This article is mainly concerned with simplices in n-dimensional hyperbolic space. The main tool is a hyperbolic version of Steiner symmetrization. Our main results are: (A) Let T be the set of all hyperbolic n-simplices in a given closed ball B. A simplex in T is of maximal volume if and only if it is regular and if its vertices are contained in the boundary of B. (B) A hyperbolic simplex is of maximal volume if and only if it is regular and ideal. (C) Let T denote the set of all finite hyperbolic simplices with inradius r. A simplex in T has minimal total edge length if and only if it is regular. (D) Let T denote the set of all finite hyperbolic simplices of volume V. A simplex in T has minimal total edge length if and only if it is regular.

Citation

Peyerimhoff, N. (2002). Simplices of maximal volume or minimal total edge length in hyperbolic space. Journal of the London Mathematical Society, 66(3), 753-768. https://doi.org/10.1112/s0024610702003629

Journal Article Type Article
Online Publication Date Oct 1, 2002
Publication Date Oct 1, 2002
Deposit Date Apr 27, 2007
Journal Journal of the London Mathematical Society
Print ISSN 0024-6107
Electronic ISSN 1469-7750
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 66
Issue 3
Pages 753-768
DOI https://doi.org/10.1112/s0024610702003629
Keywords Constant curvature.

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