Calculus of Variations and Geometric Measure Theory

A. Fathi - A. Figalli - L. Rifford

On the Hausdorff Dimension of the Mather Quotient

created by figalli on 29 Feb 2008
modified on 28 Nov 2008


Accepted Paper

Inserted: 29 feb 2008
Last Updated: 28 nov 2008

Journal: Comm. Pure Appl. Math.
Year: 2008


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 present applications in dynamics.