Some properties of the landslide flow
Event details
| Date | 15.04.2013 |
| Hour | 17:15 › 18:00 |
| Speaker | Gabriele Mondello (University of Rome) |
| Location | |
| Category | Conferences - Seminars |
Hamiltonian Dynamics Seminar
Abstract: An earthquake is a deformation of a hyperbolic metric on a surface concentrated on a simple closed curve or, more generally, on a measured geodesic lamination. Mess showed that this deformation can be interpreted by isometrically immersing the surface inside an anti-de Sitter 3-manifold with bending datum given by the measured lamination.
Generalizing this recipe, we will define the landslide, which is a deformation of a hyperbolic metric whose intensity is parametrized by another hyperbolic metric, and we will show that it is a smoother analog of the earthquake on Teichmüller space.
Similarly, we introduce the imaginary version of the landslide, the ``smooth grafting'', which generalizes the grafting along a measured lamination which is the imaginary counterpart of the earthquake (related by Thurston to bent surfaces in hyperbolic 3-manifolds).
We discuss some properties of these deformations: including the Hamiltonian nature of the landslide flow with respect to the Weil-Petersson symplectic structure, the convexity of the Hamiltonian function along Weil-Petersson geodesics, the symplectic nature of the smooth grafting and the extension of such deformation to the boundary...
This is joint work with Francesco Bonsante and Jean-Marc Schlenker.
Abstract: An earthquake is a deformation of a hyperbolic metric on a surface concentrated on a simple closed curve or, more generally, on a measured geodesic lamination. Mess showed that this deformation can be interpreted by isometrically immersing the surface inside an anti-de Sitter 3-manifold with bending datum given by the measured lamination.
Generalizing this recipe, we will define the landslide, which is a deformation of a hyperbolic metric whose intensity is parametrized by another hyperbolic metric, and we will show that it is a smoother analog of the earthquake on Teichmüller space.
Similarly, we introduce the imaginary version of the landslide, the ``smooth grafting'', which generalizes the grafting along a measured lamination which is the imaginary counterpart of the earthquake (related by Thurston to bent surfaces in hyperbolic 3-manifolds).
We discuss some properties of these deformations: including the Hamiltonian nature of the landslide flow with respect to the Weil-Petersson symplectic structure, the convexity of the Hamiltonian function along Weil-Petersson geodesics, the symplectic nature of the smooth grafting and the extension of such deformation to the boundary...
This is joint work with Francesco Bonsante and Jean-Marc Schlenker.
Practical information
- Expert
- Free
Organizer
- Martins Bruveris and Sonja Hohloch (EPFL)