Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class (2008)
Fathi, Albert, Giuliani, Alessandro, Sorrentino, Alfonso
Given a smooth compact Riemannian manifold $M$ and a Hamiltonian $H$ on the cotangent space $T^*M$, strictly convex and superlinear in the momentum variables, we prove uniqueness of certain ergodic...
Optimal transportation on non-compact manifolds (2007)
Fathi, Albert, Figalli, Alessio
In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In...
On the Hausdorff Dimension of the Mather Quotient (2007)
Fathi, Albert, Figalli, Alessio, Rifford, Ludovic
Under appropriate assumptions on the dimension of the ambient manifold and the regularity of the Hamiltonian, we show that the Mather quotient is small in term of Hausdorff dimension. Then, we...
Weak KAM theorem on non compact (2001)
Manifolds Albert Fathi, Albert Fathi, Ezequiel Maderna
We prove a weak KAM theorem for C -convex Hamiltonians on the cotangent bundle of a non-compact manifold. The Hamiltonian must be uniformly bounded on the fibers and uniformly superlinear with...
Transformations et homéomorphismes préservant la mesure : systémes dynamiques minimaux / (1980)
Thesis (doctoral)--Université Paris-Sud, 1980.