Thurston's bending measure conjecture for once punctured torus groups

TL;DR

This paper proves Thurston's conjecture that the bending measures of the convex hull boundary components uniquely determine quasifuchsian once punctured torus groups, advancing understanding of hyperbolic 3-manifolds.

Contribution

It provides a proof of Thurston's bending measure conjecture specifically for quasifuchsian once punctured torus groups, a significant case in hyperbolic geometry.

Findings

Bending measures uniquely determine the group in this setting

Confirmed Thurston's conjecture for once punctured torus groups

Enhances understanding of convex hull boundaries in hyperbolic 3-manifolds

Abstract

We prove Thurston's bending measure conjecture for quasifuchsian once punctured torus groups. The conjecture states that the bending measures of the two components of the convex hull boundary uniquely determine the group.