Calculus of Variations and Geometric Measure Theory

M. Liero - A. Mielke - G. Savaré

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

created by savare on 24 Feb 2021



Inserted: 24 feb 2021

Year: 2015

ArXiv: 1509.00068 PDF


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. We give a construction of geodesic curves and discuss their properties.