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math.DG2016
The Camassa-Holm equation as an incompressible Euler equation: a geometric point of view
Thomas Gallouët, François-Xavier Vialard
The group of diffeomorphisms of a compact manifold endowed with the L^2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler…
math.DG2014
On the convexity of injectivity domains on nonfocal manifolds
Alessio Figalli, Thomas Gallouët, Ludovic Rifford
Given a smooth nonfocal compact Riemannian manifold, we show that the so-called Ma--Trudinger--Wang condition implies the convexity of injectivity domains. This improves a previous…