Jacobian determinant inequality on corank 1 Carnot groups with applications

DOI10.1016/J.JFA.2019.108293zbMath1427.53038arXiv1701.08831OpenAlexW2966863191MaRDI QIDQ2329301

Kinga Sipos, Zoltán M. Balogh, Alexandru Kristály

Publication date: 17 October 2019

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.08831

zbMATH Keywords

Carnot groupBrunn-Minkowski inequalityoptimal mass transportationabnormal and normal geodesics

Mathematics Subject Classification ID

Sub-Riemannian geometry (53C17) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (8)

Bakry-Émery curvature and model spaces in sub-Riemannian geometry ⋮ Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries ⋮ Almost-Riemannian manifolds do not satisfy the curvature-dimension condition ⋮ Branching geodesics in sub-Riemannian geometry ⋮ Sub-Riemannian interpolation inequalities ⋮ Geometric inequalities on Heisenberg groups ⋮ Sub-Riemannian structures do not satisfy Riemannian Brunn-Minkowski inequalities ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

Cites Work

• Geodesic interpolation inequalities on Heisenberg groups
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Mass transportation on sub-Riemannian manifolds
• Finsler interpolation inequalities
• Optimal mass transportation in the Heisenberg group.
• A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
• Sub-Riemannian interpolation inequalities
• Geometric inequalities on Heisenberg groups
• Ricci curvature for metric-measure spaces via optimal transport
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• On the isoperimetric problem in the Heisenberg group \(\mathbb H^n\)
• Measure contraction properties of Carnot groups
• Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group
• Optimal transportation under nonholonomic constraints
• The Brunn-Minkowski inequality
• Optimal maps in essentially non-branching spaces
• Optimal Transport
• Polar factorization of maps on Riemannian manifolds

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