Optimal transport in competition with reaction: the HellingerKantorovich distance and geodesic curves
Abstract
We discuss a new notion of distance on the space of finite and nonnegative measures which can be seen as a generalization of the wellknown KantorovichWasserstein 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1509.00068
 Bibcode:
 2015arXiv150900068L
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Analysis of PDEs
 EPrint:
 SIAM J. Math. Analysis 48 (2016) 28692911