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.
The deformation spaces of convex RP^2-structures on 2-orbifolds
Classification of tight contact structures on a solid torus
Spaces of knots in the solid torus, knots in the thickened torus, and irreducible links in the 3-sphere
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