# Optimal Transport in Competition with Reaction: The Hellinger-Kantorovich Distance and Geodesic Curves

@article{Liero2016OptimalTI, title={Optimal Transport in Competition with Reaction: The Hellinger-Kantorovich Distance and Geodesic Curves}, author={Matthias Liero and Alexander Mielke and Giuseppe Savar{\'e}}, journal={SIAM J. Math. Anal.}, year={2016}, volume={48}, pages={2869-2911} }

We discuss a new notion of distance on the space of finite and nonnegative measures on $\Omega \subset {\mathbb R}^d$, which we call the Hellinger--Kantorovich distance. It can be seen as an inf-convolution of the well-known Kantorovich--Wasserstein distance and the Hellinger-Kakutani 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… Expand

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