Matthias Liero: On entropy transport problems and the Hellinger Kantorovich distance

In this talk, we will present a general class of variational problems involving entropy-transport minimization with respect to a couple of given finite measures with possibly unequal total mass. These optimal entropy-transport problems can be regarded as a natural generalization of classical optimal transportation problems. With an appropriate choice of the entropy/cost functionals they provide a distance between measures that exhibits interesting geometric features. We call this distance Hellinger-Kantorovich distance as it can be seen as an interpolation between the Hellinger and the Kantorovich-Wasserstein distance. The link to the entropy-transport minimization problems relies on convex duality in a surprising way. Moreover, a dynamic Benamou-Brenier characterization also shows the role of these distances in dynamic processes involving creation or annihilation of masses. Finally, we will give a characterization of geodesic curves and of convex functionals.

This is joint work with Giuseppe Savaré and Alexander Mielke.

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Follow-up Workshop to JTP Optimal Transportation (30.08.2016)