Sub-Riemannian interpolation inequalities

DOI10.1007/s00222-018-0840-yzbMath1412.53051arXiv1705.05380OpenAlexW2936930064WikidataQ115388478 ScholiaQ115388478MaRDI QIDQ1741569

Davide Barilari, Luca Rizzi

Publication date: 3 May 2019

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.05380

zbMATH Keywords

Heisenberg groupoptimal transportsub-Riemannian distancegeneralized H-type Carnot groupsgeodesic Brunn-Minkowski inequalitiessub-Riemannian Jacobi fields

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Existence theories for optimal control problems involving ordinary differential equations (49J15) Sub-Riemannian geometry (53C17)

Related Items (17)

Geodesic fields for Pontryagin type C⁰-Finsler manifolds ⋮ A direct proof of the Brunn-Minkowski inequality in nilpotent Lie groups ⋮ Bakry-Émery curvature and model spaces in sub-Riemannian geometry ⋮ Isoperimetric inequality in noncompact 𝖬𝖢𝖯 spaces ⋮ Sharp \(p\)-Poincaré inequalities under measure contraction property ⋮ The Brunn-Minkowski inequality implies the CD condition in weighted Riemannian manifolds ⋮ Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries ⋮ Almost-Riemannian manifolds do not satisfy the curvature-dimension condition ⋮ Local isoperimetric inequalities in metric measure spaces verifying measure contraction property ⋮ Branching geodesics in sub-Riemannian geometry ⋮ Sharp Poincaré inequalities under Measure Contraction Property ⋮ Sub-Riemannian structures do not satisfy Riemannian Brunn-Minkowski inequalities ⋮ Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations ⋮ Distortion coefficients of the \(\alpha\)-Grushin plane ⋮ Isoperimetric inequality under measure-contraction property ⋮ Jacobian determinant inequality on corank 1 Carnot groups with applications ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ricci curvatures in Carnot groups
• Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds
• Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries
• On the subRiemannian cut locus in a model of free two-step Carnot group
• On the Hausdorff volume in sub-Riemannian geometry
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups
• On Carnot-Caratheodory metrics
• Absolute continuity of Wasserstein geodesics in the Heisenberg group
• Semiconcavity results for optimal control problems admitting no singular minimizing controls
• A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
• Mass transportation on sub-Riemannian manifolds
• Finsler interpolation inequalities
• Differential geometry of curves in Lagrange Grassmannians with given Young diagram
• Optimal mass transportation in the Heisenberg group.
• A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
• Brunn-Minkowski inequalities in product metric measure spaces
• Geometric inequalities on Heisenberg groups
• Any sub-Riemannian metric has points of smoothness
• Morse-Sard type results in sub-Riemannian geometry
• Perturbation theory for linear operators.
• Geometry of Jacobi curves. I
• Geometry of Jacobi curves. II
• Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups
• Jacobian determinant inequality on corank 1 Carnot groups with applications
• Ricci curvature for metric-measure spaces via optimal transport
• Transverse Weitzenböck formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves
• Sub-Riemannian curvature of Carnot groups with rank-two distributions
• Displacement interpolations from a Hamiltonian point of view
• On the measure contraction property of metric measure spaces
• Genericity results for singular curves
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• On the isoperimetric problem in the Heisenberg group \(\mathbb H^n\)
• Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds.
• Measure contraction properties of Carnot groups
• Comparison theorems for conjugate points in sub-Riemannian geometry
• Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group
• Optimal transportation under nonholonomic constraints
• Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations
• Sub-Riemannian sphere in Martinet flat case
• The Brunn-Minkowski inequality
• A counterexample to gluing theorems for MCP metric measure spaces
• On the cut locus of free, step two Carnot groups
• Curvature: A Variational Approach
• Left-Invariant Sub-Riemannian Engel Structures: Abnormal Geodesics and Integrability
• Sharp measure contraction property for generalized H-type Carnot groups
• On Jacobi fields and a canonical connection in sub-Riemannian geometry
• Sub-Riemannian Geometry and Optimal Transport
• Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
• Optimal Transport
• Polar factorization of maps on Riemannian manifolds

This page was built for publication: Sub-Riemannian interpolation inequalities