Continuity of the Volume of Simplices in Classical Geometry

2004/12/10 by Feng Luo, Luo, Feng
Mathematics · Physics and Astronomy · #53A35 #53C65 #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #History and Theory of Mathematics #Mathematical Physics (math-ph) #Mathematics and Applications #Metric Geometry (math.MG) #math-ph #math.GT #math.MG #math.MP #msc:53A35 #msc:53C65

paper · pdf · doi:10.48550/arxiv.math/0412208

19 pages

arxiv created 2004/12/10 · openalex publication_date 2004/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Continuity of volumes -- on a generalization of a conjecture of J. W. Milnor
• Volumes and degeneration -- on a conjecture of J. W. Milnor
• Comparing Corresponding Dihedral Angles on Classical Geometric Simplices
• Volumes of Regular Hyperbolic Simplices
• Volume form as volume of infinitesimal simplices