Deforming ideal solid tori

TL;DR

This paper characterizes the deformation space of ideal solid tori with boundary modeled on convex hyperbolic polyhedra, extending to singular cases, using a volume maximization approach based on tetrahedral decomposition.

Contribution

It introduces a new description of the deformation space for ideal solid tori with boundary and singularities, using Gauss-Bonnet inequalities and volume maximization.

Findings

Deformation space characterized by Gauss-Bonnet inequalities.

Extension to tori with conical singularities.

Method based on tetrahedral decomposition and volume maximization.

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.