The co-Minkowski space and an asymmetric norm on the Teichmüller space
Abstract: W.P. Thurston has defined two assymetric norm on the Teichmüller space. The most famous is the one related to the minimization problem of the Lipschitz constant of a map between two hyperbolic surfaces. In the same paper, he also defined another one, dual to the first one in some meaning, which is defined as the length of measured geodesic laminations, once identified in the correct way tangent vectors with measured geidesic laminations. I will show that this construction can be generalized to some assymetric Finsler norm on $H^1(G, R^{1,n})$ where $G$ is a cocompact lattice of $SO(1,n)$. I will also comment on an useful tool related to this: the co-Minkowski space, i.e. the space of spacelike hyperplanes in the Minkowski space.
This is a work in collaboration with F. Fillastre.