# Earthquakes and graftings of hyperbolic surface laminations

## TL;DR

This paper explores the deformation theory of hyperbolic surface laminations, revealing their Teichmüller spaces are infinite-dimensional and introducing a new formula for geodesic length derivatives related to grafting.

## Contribution

It introduces a novel formula for the derivative of geodesic lengths under grafting, extending the understanding of hyperbolic surface lamination deformations.

## Key findings

- Teichmüller space of hyperbolic surface laminations is infinite dimensional
- Derived a new formula for geodesic length derivatives under grafting
- Extended deformation theory in hyperbolic geometry

## Abstract

We study compact hyperbolic surface laminations. These are a generalization of closed hyperbolic surfaces which appear to be more suited to the study of Teichm\"uller theory than arbitrary non-compact surfaces. We show that the Teichm\"uller space of any non-trivial hyperbolic surface lamination is infinite dimensional. In order to prove this result, we study the theory of deformations of hyperbolic surfaces, and we derive what we believe to be a new formula for the derivative of the length of a simple closed geodesic with respect to the action of grafting. This formula complements those derived by McMullen in [23], in terms of the Weil-Petersson metric, and by Wolpert in [33], for the case of earthquakes.