On a Conjecture of Milnor about Volume of Simplexes

2005/10/31 by Ren Guo, Feng Luo, Guo, Ren +1
Computer Science · Mathematics · #53A35 #53C65 #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #Matrix Theory and Algorithms #Metric Geometry (math.MG) #math.GT #math.MG #msc:53A35 #msc:53C65

paper · pdf · doi:10.48550/arxiv.math/0510666

15 pages. Version for publication

openalex publication_date 2005/10/31 · arxiv created 2007/08/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the second part of Milnor's conjecture on the volume of simplexes in hyperbolic and spherical spaces. A characterization of the closure of the space of the angle Gram matrices of simplexes is also obtained.

Related

• Continuity of volumes -- on a generalization of a conjecture of J. W. Milnor
• Volumes and degeneration -- on a conjecture of J. W. Milnor
• Volumes of Regular Hyperbolic Simplices
• On the volume growth of the hyperbolic regular n-simplex
• Inégalités de Milnor-Wood géométriques