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Title: Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures
Authors: Laschos, VaiosMielke, Alexander
Publishers Version: https://doi.org/10.20347/WIAS.PREPRINT.2458
Issue Date: 2017
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2458, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: 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.
Keywords: Geometry on cones; local angle condition; K-semiconcavity; Hellinger-Kantorovich; Spherical Hellinger-Kantorovich
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



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