  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.
