113 citations · 350 across the 9 of their papers we have counts for
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math.OC2007★ 5 cited
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…
math.DS2007
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…