Monge's transport problem in the Heisenberg group

DOI10.1515/ACV.2010.026zbMath1216.49039arXiv1001.4012OpenAlexW2962799346MaRDI QIDQ2999542

Séverine Rigot, Luigi De Pascale

Publication date: 13 May 2011

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.4012

zbMATH Keywords

Heisenberg groupMonge transport problemMonge-Kantorovich problemoptimal transport mapsub-Riemannian distance

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Sub-Riemannian geometry (53C17)

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Cites Work

• The Monge problem for strictly convex norms in \(\mathbb R^d\)
• Absolute continuity of Wasserstein geodesics in the Heisenberg group
• Absolute continuity and summability of transport densities: simpler proofs and new estimates
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Optimal mass transportation in the Heisenberg group.
• Existence of optimal transport maps for crystalline norms
• Asymptotic development by \(\Gamma{}\)-convergence
• Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs
• Monge’s transport problem on a Riemannian manifold