Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves

Understand

We discuss a new notion of distance on the space of finite and nonnegative measures which can be seen as a generalization of the well-known Kantorovich-Wasserstein distance.

• The new distance is based on a dynamical formulation given by an Onsager operator that is the sum of a Wasserstein diffusion part and an additional reaction part describing the generation and absorption of mass.
• We present a full characterization of the distance and its properties.
• In fact the distance can be equivalently described by an optimal transport problem on the cone space over the underlying metric space.