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- W2811358037 abstract "We study geodesic equations for a family of right-invariant Riemannian metrics on the group of diffeomorphisms of a compact manifold. The metrics descend to Fisher's information metric on the space of smooth probability densities. The right reduced geodesic equations are higher-dimensional generalisations of the $mu$--Hunter--Saxton equation, used to model liquid crystals under influence of magnetic fields. Local existence and uniqueness results are established by proving smoothness of the geodesic spray. The descending property of the metrics is used to obtain a novel factorisation of diffeomorphisms. Analogous to the polar factorisation in optimal mass transport, this factorisation solves an optimal information transport problem. It can be seen as an infinite-dimensional version of $QR$ factorisation of matrices." @default.
- W2811358037 created "2018-07-10" @default.
- W2811358037 creator A5052120629 @default.
- W2811358037 date "2012-03-20" @default.
- W2811358037 modified "2023-09-26" @default.
- W2811358037 title "Generalised Hunter-Saxton equations and descending metrics on diffeomorphism groups" @default.
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