Almost-Riemannian manifolds do not satisfy the curvature-dimension condition

DOI10.1007/s00526-023-02466-xOpenAlexW4327981257WikidataQ125857524 ScholiaQ125857524MaRDI QIDQ2695760

Mattia Magnabosco, Tommaso Rossi

Publication date: 5 April 2023

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.08775

zbMATH Keywords

curvature-dimension conditionalmost-Riemannian manifolds

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Geodesics in global differential geometry (53C22) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Sub-Riemannian geometry (53C17)

Related Items

Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries

Uses Software

• GitHub

Cites Work

• Unnamed Item
• Local properties of almost-Riemannian structures in dimension 3
• On the essential self-adjointness of singular sub-Laplacians
• A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
• Quantum confinement on non-complete Riemannian manifolds
• Regularity results for the minimum time function with Hörmander vector fields
• Sub-Riemannian interpolation inequalities
• Definitions of Sobolev classes on metric spaces
• Control theory from the geometric viewpoint.
• Sub-Riemannian structures do not satisfy Riemannian Brunn-Minkowski inequalities
• Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups
• Branching geodesics in sub-Riemannian geometry
• The globalization theorem for the curvature-dimension condition
• Jacobian determinant inequality on corank 1 Carnot groups with applications
• Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
• Ricci curvature for metric-measure spaces via optimal transport
• Monge problem in metric measure spaces with Riemannian curvature-dimension condition
• 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
• Measure contraction properties of Carnot groups
• New formulas for the Laplacian of distance functions and applications
• The Quasi Curvature‐Dimension Condition with Applications to Sub‐Riemannian Manifolds
• Curvature: A Variational Approach
• Sharp measure contraction property for generalized H-type Carnot groups
• A Comprehensive Introduction to Sub-Riemannian Geometry