Deforming ideal solid tori

2009/11/16 by François Guéritaud, Guéritaud, François
Engineering · Mathematics · #57M50 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M50

paper · pdf · doi:10.48550/arxiv.0911.3067

15 pages, 0 figures

arxiv created 2009/11/16 · openalex publication_date 2009/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We describe the deformation space of a solid torus with boundary modelled on convex ideal hyperbolic polyhedra. This deformation space is given by natural Gauss--Bonnet type inequalities on the dihedral angles. The result extends to solid tori with an arbitrary conical singularity along the core. Our method is to decompose the torus into tetrahedra and maximize a volume functional.

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