A cyclic extension of the earthquake flow

Abstract

Let $\cT$ be Teichmüller space of a closed surface of genus at least 2. For any point $c\in \cT$, we describe an action of the circle on $\cT\times \cT$, which limits to the earthquake flow when one of the parameters goes to a measured lamination in the Thurston boundary of $\cT$. This circle action shares some of the main properties of the earthquake flow, for instance it satisfies an extension of Thurston's Earthquake Theorem and it has a complex extension which is analogous and limits to complex earthquakes. Moreover, a related circle action on $\cT\times \cT$ extends to the product of two copies of the universal Teichmüller space.

39 pages, 5 figures

References in corpus (3)

• On the renormalized volume of hyperbolic 3-manifolds
• Minimal surfaces and particles in 3-manifolds
• Projective structures, grafting, and measured laminations

Cited by in corpus (4)

• Area-preserving diffeomorphism of the hyperbolic plane and K-surfaces in Anti-de Sitter space
• Polynomial cubic differentials and convex polygons in the projective plane
• Bending laminations on convex hulls of anti-de Sitter quasicircles
• Constant scalar curvature hypersurfaces in $(3+1)$-dimensional GHMC Minkowski spacetimes