Optimal transportation under nonholonomic constraints

DOI10.1090/S0002-9947-09-04813-2zbMath1175.49037arXiv0710.0408MaRDI QIDQ3642702

Paul W. Y. Lee, Andrei A. Agrachev

Publication date: 6 November 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.0408

zbMATH Keywords

abnormal minimizersMonge's optimal transportation problemsubriemannian manifolds

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Existence theories for optimal control problems involving partial differential equations (49J20) Sub-Riemannian geometry (53C17)

Related Items (24)

Franks' lemma for \(C^2\)-Mañé perturbations of Riemannian metrics and applications to persistence ⋮ Geodesic fields for Pontryagin type C⁰-Finsler manifolds ⋮ Optimal controlled transports with free end times subject to import/export tariffs ⋮ Every sub-Riemannian manifold is the Gromov-Hausdorff limit of a sequence Riemannian manifolds ⋮ Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry ⋮ Dynamical optimal transport of nonlinear control-affine systems ⋮ Mass transportation with LQ cost functions ⋮ On the Set of Points of Smoothness for the Value Function of Affine Optimal Control Problems ⋮ A remark on the potentials of optimal transport maps ⋮ Optimal Transport with Controlled Dynamics and Free End Times ⋮ Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds ⋮ Optimal transport over nonlinear systems via infinitesimal generators on graphs ⋮ Mass transportation on sub-Riemannian structures of rank two in dimension four ⋮ Sub-Riemannian interpolation inequalities ⋮ On the subRiemannian cut locus in a model of free two-step Carnot group ⋮ The Ma-Trudinger-Wang curvature for natural mechanical actions ⋮ Mass transportation on sub-Riemannian manifolds ⋮ Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups ⋮ Sharp measure contraction property for generalized H-type Carnot groups ⋮ Existence of optimal transport maps in very strict \(CD(K,\infty)\) -spaces ⋮ Jacobian determinant inequality on corank 1 Carnot groups with applications ⋮ Optimal transportation, topology and uniqueness ⋮ Optimal transportation in \(\mathbb R^n\) for a distance cost with a convex constraint ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

Cites Work

• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Optimal mass transportation and Mather theory
• Semiconcavity results for optimal control problems admitting no singular minimizing controls
• Optimal mass transportation in the Heisenberg group.
• Control theory from the geometric viewpoint.
• Strong minimality of abnormal geodesics for \(2\)-distributions
• Abnormal sub-Riemannian geodesics: Morse index and rigidity
• Polar factorization and monotone rearrangement of vector‐valued functions
• Abnormal Minimizers
• Shortest paths for sub-Riemannian metrics on rank-two distributions
• Existence, Uniqueness, and Regularity of Optimal Transport Maps
• Optimal Transport
• On the subanalyticity of Carnot-Carathéodory distances
• Polar factorization of maps on Riemannian manifolds
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Optimal transportation under nonholonomic constraints