Results 11 to 20 of about 33,682 (168)

Sub-Riemannian Geometry on Infinite-Dimensional Manifolds [PDF]

The Journal of Geometric Analysis, 2014
We generalize the concept of sub-Riemannian geometry to infinite-dimensional manifolds modeled on convenient vector spaces. On a sub-Riemannian manifold $M$, the metric is defined only on a sub-bundle $\calH$ of the tangent bundle $TM$, called the horizontal distribution.
Grong, Erlend, Markina, Irina, Vasil'ev, Alexander   +2 more
openaire   +4 more sources

Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry [PDF]

Advances in Mathematics, 2017
On a sub-Riemannian manifold we define two type of Laplacians. The \emph{macroscopic Laplacian} $\Delta_\omega$, as the divergence of the horizontal gradient, once a volume $\omega$ is fixed, and the \emph{microscopic Laplacian}, as the operator ...
Boscain, Ugo, Neel, Robert, Rizzi, Luca
core   +6 more sources

Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations, Part I [PDF]

Mathematische Zeitschrift, 2015
We give a generalized curvature-dimension inequality connecting the geometry of sub-Riemannian manifolds with the properties of its sub-Laplacian. This inequality is valid on a large class of sub-Riemannian manifolds obtained from Riemannian foliations ...
Grong, Erlend, Thalmaier, Anton
core   +7 more sources

A contact covariant approach to optimal control with applications to sub-Riemannian geometry [PDF]

Mathematics of Control, Signals, and Systems, 2016
We discuss contact geometry naturally related with optimal control problems (and Pontryagin Maximum Principle). We explore and expand the observations of [Ohsawa, 2015], providing simple and elegant characterizations of normal and abnormal sub-Riemannian
Jóźwikowski, Michał, Respondek, Witold   +1 more
core   +4 more sources

Constant curvature models in sub-Riemannian geometry

Journal of Geometry and Physics, 2019
The second version reflected comments from the reviewing process. Introduction and parts of exposition are extended, some proofs made more precise.
Alekseevsky, D., Medvedev, A., Slovak, J.   +2 more
openaire   +5 more sources

Shortest and straightest geodesics in sub-Riemannian geometry [PDF]

Journal of Geometry and Physics, 2020
There are many equivalent definitions of Riemannian geodesics. They are naturally generalised to sub-Riemannian manifold, but become non-equivalent. We give a review of different definitions of geodesics of a sub-Riemannian manifold and interrelation between them.
Dmitri Alekseevsky
openaire   +5 more sources

Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry [PDF]

SIAM Journal on Applied Mathematics, 2018
From the point of view of the theory of the partial differential equations, the paper is concerned with the Helmholtz version of the Grushin equation \[ (\partial^2_x+ x^{2r}\partial^2_y) u+ \rho^2u= 0,\quad r=1,2,\dots, \] which, by separation of variables, reduces to the analysis of eigenfunctions of anisotropic harmonic oscillators.
Greenleaf, A, Kettunen, H, Kurylev, Y, Lassas, M, Uhlmann, G   +4 more
openaire   +4 more sources

Multi-Frequency Image Completion via a Biologically-Inspired Sub-Riemannian Model with Frequency and Phase

Journal of Imaging, 2021
We present a novel cortically-inspired image completion algorithm. It uses five-dimensional sub-Riemannian cortical geometry, modeling the orientation, spatial frequency and phase-selective behavior of the cells in the visual cortex.
Emre Baspinar
doaj   +1 more source

Integral Formulas for a Foliation with a Unit Normal Vector Field

Mathematics, 2021
In this article, we prove integral formulas for a Riemannian manifold equipped with a foliation F and a unit vector field N orthogonal to F, and generalize known integral formulas (due to Brito-Langevin-Rosenberg and Andrzejewski-Walczak) for foliations ...
Vladimir Rovenski
doaj   +1 more source

The Sub-Riemannian Limit of Curvatures for Curves and Surfaces and a Gauss-Bonnet Theorem in the Group of Rigid Motions of Minkowski Plane with General Left-Invariant Metric

Journal of Function Spaces, 2021
The group of rigid motions of the Minkowski plane with a general left-invariant metric is denoted by E1,1,gλ1,λ2, where λ1≥λ2>0. It provides a natural 2-parametric deformation family of the Riemannian homogeneous manifold Sol3=E1,1,g1,1 which is the ...
Jianyun Guan, Haiming Liu
doaj   +1 more source