WIAS Preprint No. 2973, (2022)

Evolutionary variational inequalities on the Hellinger--Kantorovich and spherical Hellinger--Kantorovich spaces


  • Laschos, Vaios
    ORCID: 0000-0001-8721-5335
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2020 Mathematics Subject Classification

  • 28A33 54E35 49Q2 49J35 49J40 49K35 46G99


  • Hellinger distance, Wasserstein distance, minimizing movement scheme, geodesic semiconvexity, evolutionary variational inequality




We study the minimizing movement scheme for families of geodesically semiconvex 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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