Lipschitz classification of almost-Riemannian distances on compact oriented surfaces

DOI10.1007/s12220-011-9262-4zbMath1259.53031arXiv1003.4842OpenAlexW1972616956WikidataQ115376886 ScholiaQ115376886MaRDI QIDQ1935489

R. Ghezzi, Ugo V. Boscain, Mario Sigalotti, Gregoire Charlot

Publication date: 18 February 2013

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4842

zbMATH Keywords

sub-Riemannian geometryCarnot-Carathéodory distanceLipschitz equivalencealmost-Riemannian surface

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Sub-Riemannian geometry (53C17)

Related Items (12)

Solvable approximations of 3-dimensional almost-Riemannian structures ⋮ Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces ⋮ Almost-Riemannian structures on nonnilpotent, solvable 3D Lie groups ⋮ Quantum confinement for the curvature Laplacian \(- \Delta + cK\) on 2D-almost-Riemannian manifolds ⋮ Closure of the Laplace-Beltrami operator on 2D almost-Riemannian manifolds and semi-Fredholm properties of differential operators on Lie manifolds ⋮ The Laplace-Beltrami operator in almost-Riemannian geometry ⋮ Metrics with equatorial singularities on the sphere ⋮ Local contact sub-Finslerian geometry for maximum norms in dimension 3 ⋮ On the Whitney extension property for continuously differentiable horizontal curves in sub-Riemannian manifolds ⋮ Isometries of almost-Riemannian structures on Lie groups ⋮ Almost-Riemannian Geometry on Lie Groups ⋮ Local properties of almost-Riemannian structures in dimension 3

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry
• Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy
• A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
• Two-dimensional almost-Riemannian structures with tangency points
• Quasi-homogeneous blowing-ups
• Control theory from the geometric viewpoint.
• Conjugate and cut loci of a two-sphere of revolution with application to optimal control
• The Laplace-Beltrami operator in almost-Riemannian geometry
• Optimal control in laser-induced population transfer for two- and three-level quantum systems

This page was built for publication: Lipschitz classification of almost-Riemannian distances on compact oriented surfaces