Earthquakes and graftings of hyperbolic surface laminations

Álvarez, Sebastien - Smith, Graham

Resumen:

We study compact hyperbolic surface laminations. These are a generalization of closed hyperbolic surfaces which appear to be more suited to the study of Teichmüller theory than arbitrary non-compact surfaces. We show that the Teichmüller 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.


Detalles Bibliográficos
2019
ANII: FCE_3_2018_1_148740
Differential Geometry
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/35003
Acceso abierto
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)