Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures

DOI10.1016/j.jfa.2018.12.013zbMath1422.60009arXiv1712.01888OpenAlexW2963958758WikidataQ128606479 ScholiaQ128606479MaRDI QIDQ1738997

Alexander Mielke, Vaios Laschos

Publication date: 24 April 2019

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.01888

zbMATH Keywords

Hellinger-Kantorovich spaceK-semiconcavitylocal angle conditionspherical Hellinger-Kantorovich space

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of measures, convergence of measures (28A33)

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A new transportation distance with bulk/interface interactions and flux penalization ⋮ Birth–death dynamics for sampling: global convergence, approximations and their asymptotics ⋮ Hellinger–Kantorovich barycenter between Dirac measures ⋮ Fine properties of geodesics and geodesic \(\lambda\)-convexity for the Hellinger-Kantorovich distance ⋮ A machine learning framework for geodesics under spherical Wasserstein-Fisher-Rao metric and its application for weighted sample generation ⋮ On Optimal Transport of Matrix-Valued Measures ⋮ The Schrödinger problem on the non-commutative Fisher-Rao space ⋮ Gradient flows and evolution variational inequalities in metric spaces. I: structural properties ⋮ Convex Sobolev inequalities related to unbalanced optimal transport ⋮ Barycenters for the Hellinger--Kantorovich Distance Over $\mathbb{R}^d$ ⋮ Spherical Hellinger--Kantorovich Gradient Flows ⋮ The Linearized Hellinger--Kantorovich Distance

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