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Evolutionary Variational Inequalities on the Hellinger-Kantorovich and Spherical Hellinger-Kantorovich spaces

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arxiv 2207.09815 v3 pith:4MTRF5AJ submitted 2022-07-20 math.AP

Vaios Laschos , Alexander Mielke This is my paper · ORCID
classification math.AP
keywords hellinger-kantorovichcurvesevolutionarygeodesicallyminimizingmovementschemespaces
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We study the minimizing movement scheme for families of geodesically semi-convex functionals defined on either the Hellinger-Kantorovich or the Spherical Hellinger-Kantorovich space. By exploiting some of the finer geometric properties of those spaces, we prove that the sequence of curves, which are produced by geodesically interpolating the points generated by the minimizing movement scheme, converges to curves that satisfy the Evolutionary Variational Inequality (EVI), when the time step goes to 0.

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Cited by 1 Pith paper

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  1. Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow

    math.AP 2025-04 conditional novelty 7.0 of 10

    The HK-Boltzmann gradient flow preserves Gaussianity, and the reduced equations for mean, covariance, and mass admit exponential convergence rates with explicit dependence on the geometry parameters.

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