Preprint
Earthquakes and graftings of hyperbolic surface laminations
Fecha
2019Registro en:
Álvarez, S. "Earthquakes and graftings of hyperbolic surface laminations" [Preprint]. Publicado en: Mathematics (Differential Geometry). 2019, arXiv:1907.12126, Jul 2019, pp 1-27.
10.48550/arXiv.1907.12126
Autor
Álvarez, Sebastien
Smith, Graham
Institución
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.