Absolute continuity of Wasserstein geodesics in the Heisenberg group
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Publication:935048
DOI10.1016/j.jfa.2008.03.006zbMath1246.53049OpenAlexW1982194000WikidataQ112632386 ScholiaQ112632386MaRDI QIDQ935048
Alessio Figalli, Nicolas Juillet
Publication date: 31 July 2008
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2008.03.006
Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Nilpotent and solvable Lie groups (22E25) Sub-Riemannian geometry (53C17)
Related Items (12)
Geodesic interpolation inequalities on Heisenberg groups ⋮ Optimal maps in essentially non-branching spaces ⋮ Monge's transport problem in the Heisenberg group ⋮ Sub-Riemannian interpolation inequalities ⋮ Wasserstein barycenters over Riemannian manifolds ⋮ Heat Flow on Alexandrov Spaces ⋮ Geometric inequalities on Heisenberg groups ⋮ Mass transportation on sub-Riemannian manifolds ⋮ Sharp measure contraction property for generalized H-type Carnot groups ⋮ Diffusion by optimal transport in Heisenberg groups ⋮ Absolute continuity and summability of transport densities: simpler proofs and new estimates ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups
Cites Work
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- An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
- Weak curvature conditions and functional inequalities
- Optimal mass transportation in the Heisenberg group.
- Ricci curvature for metric-measure spaces via optimal transport
- On the measure contraction property of metric measure spaces
- On the geometry of metric measure spaces. I
- On the geometry of metric measure spaces. II
- Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group
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