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Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: Geometry on cones ×

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    Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Laschos, Vaios; Mielke, Alexander
    By studying general geometric properties of cone spaces, we prove the existence of a distance on the space of Probability measures that turns the Hellinger--Kantorovich space into a cone space over the space of probabilities measures. Here we exploit a natural two-parameter scaling property of the Hellinger-Kantorovich distance. For the new space, we obtain a full characterization of the geodesics. We also provide new geometric properties for the original space, including a two-parameter rescaling and reparametrization of the geodesics, local-angle condition and some partial K-semiconcavity of the squared distance, that it will be used in a future paper to prove existence of gradient flows.