Geometry of diffeomorphism groups, complete integrability and optimal transport

Boris Khesin, Jonatan Lenells, Gerard Misiolek +1

We study the geometry of the space of densities $\VolM$, which is the quotient space $\Diff(M)/\Diff_μ(M)$ of the diffeomorphism group of a compact manifold $M$ by the subgroup of…