Earthquakes and graftings of hyperbolic surface laminations
Differential Geometry
2019-07-30 v1
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.
Keywords
Cite
@article{arxiv.1907.12126,
title = {Earthquakes and graftings of hyperbolic surface laminations},
author = {Sébastien Alvarez and Graham Smith},
journal= {arXiv preprint arXiv:1907.12126},
year = {2019}
}