S. Kondratyev, D. Vorotnikov. Spherical Hellinger-Kantorovich gradient flows, SIAM J. Math. Anal 51 (2019) 2053–2084.

On p. 2082 it is claimed that the entropy E₁ is geodesically convex in the conic Hellinger-Kantorovich space for positive alpha; however, this entropy is merely geodesically semiconvex.