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arXiv · 1809.03430

Spherical Hellinger-Kantorovich gradient flows

Stanislav Kondratyev·Dmitry Vorotnikov
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Abstract

We study nonlinear degenerate parabolic equations of Fokker-Planck type which can be viewed as gradient flows with respect to the recently introduced spherical Hellinger-Kantorovich distance. The driving entropy is not assumed to be geodesically convex. We prove solvability of the problem and the entropy-entropy production inequality, which implies exponential convergence to the equilibrium. As a corollary, we obtain some related results for the Wasserstein gradient flows. We also deduce transportation inequalities in the spirit of Talagrand, Otto and Villani for the spherical and conic Hellinger-Kantorovich distances.

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Stanislav Kondratyev, Dmitry Vorotnikov. 2018-09-10. Spherical Hellinger-Kantorovich gradient flows. https://arxiv.org/abs/1809.03430

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