Related papers: Some remarks on bounded earthquakes

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…

The Teichm\"uller space $\mathcal{T}_S(\mathbf{b})$ of hyperbolic metrics on a surface $S$ with fixed lengths at the boundary components is symplectic. We prove that any sum of infinitesimal earthquakes on $S$ that is tangent to…

Given a hyperbolic surface and a simple closed geodesic on it, complex-twists along the curve produce a holomorphic family of deformations in Teichm\"{u}ller space, degenerating to the Riemann surface where it is pinched. We show there is a…

This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal stretch maps) and geodesics for the `Lipschitz metric' are constructed.…

We consider the asymptotic behavior of properly embedded minimal surfaces in the product of the hyperbolic plane with the line, taking into account the fact that there is more than one natural compactification of this space. This provides a…

A measured laminations on the universal hyperbolic solenoid $\S$ is, by our definition, a leafwise measured lamination with appropriate continuity for the transverse variations. An earthquakes on theuniversal hyperbolic solenoid $\S$ is…

Let S be a closed surface of genus at least 2, and consider two measured geodesic laminations that fill S. Right earthquakes along these laminations are diffeomorphisms of the Teichm\"uller space of S. We prove that the composition of these…

We prove an "Earthquake Theorem" for hyperbolic metrics with geodesic boundary on a compact surfaces $S$ with boundary: given two hyperbolic metrics with geodesic boundary on a surface with $k$ boundary components, there are $2^k$ right…

We give a proof of an unpublished result of Thurston showing that given any hyperbolic metric on a surface of finite type with nonempty boundary, there exists another hyperbolic metric on the same surface for which the lengths of all simple…

We give a short proof of the fact that bounded earthquakes of the unit disk induce quasisymmetric maps of the unit circle. By a similar method, we show that symmetric maps are induced by bounded earthquakes with asymptotically trivial…

In the spirit of Otal and Croke, we prove that a negatively-curved asymptotically hyperbolic surface is boundary distance rigid, where the distance between two points on the boundary at infinity is defined by a renormalized quantity.

We prove that the bijective correspondence between the space of bounded measured laminations $ML_b(\mathbb{H})$ and the universal Teichm\"uller space $T(\mathbb{H})$ given by $\lambda\mapsto E^{\lambda}|_{S^1}$ is a homeomorphism for the…

Let $\lambda_-$ and $\lambda_+$ be two bounded measured laminations on the hyperbolic disk $\mathbb H^2$, which "strongly fill" (definition below). We consider the left earthquakes along $\lambda_-$ and $\lambda_+$, considered as maps from…

We prove that all hierarchically hyperbolic spaces have finite asymptotic dimension and obtain strong bounds on these dimensions. One application of this result is to obtain the sharpest known bound on the asymptotic dimension of the…

We prove two related results. The first is an ``Earthquake Theorem'' for closed hyperbolic surfaces with cone singularities where the total angle is less than $\pi$: any two such metrics in are connected by a unique left earthquake. The…

We characterization hyperbolic metrics on compact surfaces with boundary using a variational principle. As a consequence, a new parametrization of the Teichmuller space of compact surface with boundary is produced. In the new…

We study earthquake deformations on Teichm\"uller space associated with simple closed curves of the once-punctured torus. We describe two methods to get an explicit form of the earthquake deformation for any simple closed curve. The first…

Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…

Let $X_0$ be a complete hyperbolic surface of infinite type that has a geodesic pants decomposition with cuff lengths bounded above. The length spectrum Teichm\"uller space $T_{ls}(X_0)$ consists of homotopy classes of hyperbolic metrics on…

We consider a magnetic Laplacian on a geometrically finite hyperbolic surface, when the corresponding magnetic field is infinite at the boundary at infinity. We prove that the counting function of the eigenvalues has a particular asymptotic…