Realisation of bending measured laminations by Kleinian surface groups

TL;DR

This paper extends the existence results of bending measured laminations from geometrically finite to all Kleinian surface groups, including infinite ones, and proves compactness of the realization set.

Contribution

It generalizes the existence part of the bending lamination conjecture to all Kleinian surface groups and establishes compactness of the realization set, independent of previous proofs.

Findings

Extended existence of bending laminations to infinite groups

Proved compactness of the set of groups realizing fixed laminations

Provided an independent proof from Bonahon and Otal's work

Abstract

For geometrically finite Kleinian surface groups, Bonahon and Otal proved the existence part, and partly the uniqueness part of the bending lamination conjecture. In this paper, we generalise the existence part to general Kleinian surface groups including geometrically infinite ones. We furthermore prove the compactness of the set of Kleinian surface groups realising an arbitrarily fixed data of bending laminations and ending laminations. Our proof is independent of that of Bonahon and Otal.