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

Peyerimhoff, N.

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.
• Public URL: https://durham-repository.worktribe.com/output/1567511