Volume maximization and the extended hyperbolic space
Given an angle structure on a triangulation of a 3-manifold, Casson-Rivin (for a 3-manifold with torus boundary) and Luo (for closed 3 manifolds) defined a naturally associated hyperbolic volume.NEWLINENEWLINEIn the paper under review, the authors investigate the relationship between the critical points of the volume functional and a natural extension of hyperbolic space by de Sitter space. They show that many of the critical points have geometric meaning (e.g. the existence of a spherical metric) in terms of geometric structures based on the extended hyperbolic space.
scientific article; zbMATH DE number 6024113