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Explore a lecture on entropy transport problems and the Hellinger Kantorovich distance presented by Matthias Liero at the Hausdorff Center for Mathematics. Delve into a general class of variational problems involving entropy-transport minimization with respect to finite measures of potentially unequal total mass. Discover how these optimal entropy-transport problems generalize classical optimal transportation problems and create a distance between measures with interesting geometric features. Understand the interpolation between Hellinger and Kantorovich-Wasserstein distances, and learn about the surprising link to entropy-transport minimization through convex duality. Examine the dynamic Benamou-Brenier characterization and its role in processes involving mass creation or annihilation. Gain insights into the characterization of geodesic curves and convex functionals. This 43-minute talk, part of the Follow-up Workshop to JTP Optimal Transportation, presents joint work with Giuseppe Savaré and Alexander Mielke.
