A Note on the Differentiability of the Hellinger–Kantorovich Distances.

This paper will deal with differentiability properties of the class of Hellinger–Kantorovich distances HK Λ , Σ (Λ , Σ > 0) which was recently introduced on the space M (R d) of finite nonnegative Radon measures. The derivatives of t ↦ HK Λ , Σ (μ t , ν t) 2 , for absolutely continuous curves (μ t) t , (ν t) t in (M (R d) , HK Λ , Σ) , will be computed L 1 -a.e.. The characterization of absolutely continuous curves in (M (R d) , HK Λ , Σ) will be refined. [ABSTRACT FROM AUTHOR]