Skinning bounds along thick rays

TL;DR

This paper proves that the diameter of the skinning map for acylindrical hyperbolic 3-manifolds remains bounded along thick Teichmüller geodesic rays, depending only on the ray's thickness and boundary topology.

Contribution

It establishes a uniform bound on the skinning map diameter for a class of hyperbolic 3-manifolds along thick geodesic rays, linking geometric and topological properties.

Findings

Bounded skinning map diameter along thick rays.

Dependence of bounds only on thickness and boundary topology.

Advancement in understanding hyperbolic 3-manifold geometry.

Abstract

We show that the diameter of the skinning map of an acylindrical hyperbolic 3-manifold M is bounded on thick Teichmueller geodesic rays by a constant depending only on the thickness of the ray and the topological type of the boundary of M.