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Optimal transportation on non-compact manifolds
Albert Fathi, Alessio Figalli
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 compa…
On the Hausdorff Dimension of the Mather Quotient
Albert Fathi, Alessio Figalli, Ludovic Rifford
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 dimensi…
Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index
Alberto Abbondandolo, Alessio Figalli
We study the properties of the asymptotic Maslov index of invariant measures for time-periodic Hamiltonian systems on the cotangent bundle of a compact manifold M. We show that if…
Geodesics in the space of measure-preserving maps and plans
L. Ambrosio, A. Figalli
We study Brenier's variational models for incompressible Euler equations. These models give rise to a relaxation of the Arnold distance in the space of measure-preserving maps and,…