Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups

DOI10.5802/aif.3362zbMath1477.53048arXiv1712.09900OpenAlexW3153684863WikidataQ115159001 ScholiaQ115159001MaRDI QIDQ2027768

Ludovic Rifford, Zeinab Badreddine

Publication date: 28 May 2021

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09900

zbMATH Keywords

smooth measuresub-Riemannian manifoldmeasure contractionminimizing Sard conjecturenegligeable cut loci

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Sub-Riemannian geometry (53C17)

Related Items (4)

Bakry-Émery curvature and model spaces in sub-Riemannian geometry ⋮ Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry ⋮ Almost-Riemannian manifolds do not satisfy the curvature-dimension condition ⋮ Sub-Riemannian interpolation inequalities

Cites Work

• Unnamed Item
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• Ricci curvatures in Carnot groups
• Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds
• \(p\)-adic and real subanalytic sets
• 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
• Existence and uniqueness of optimal transport maps
• Semiconcavity results for optimal control problems admitting no singular minimizing controls
• Mass transportation on sub-Riemannian manifolds
• The Sard conjecture on Martinet surfaces
• Mass transportation on sub-Riemannian structures of rank two in dimension four
• Any sub-Riemannian metric has points of smoothness
• Ricci curvature for metric-measure spaces via optimal transport
• On the curvature and heat flow on Hamiltonian systems
• 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
• Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds.
• Measure contraction properties of Carnot groups
• Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group
• Optimal transportation under nonholonomic constraints
• Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity
• Curvature: A Variational Approach
• Sharp measure contraction property for generalized H-type Carnot groups
• Some open problems
• Sub-Riemannian Geometry and Optimal Transport
• Optimal Transport
• On measure contraction property without Ricci curvature lower bound

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