C-R Immersions and Sub-Riemannian Geometry [PDF]
Axioms, 2023 On any strictly pseudoconvex CR manifold M, of CR dimension n, equipped with a positively oriented contact form θ, we consider natural ϵ-contractions, i.e., contractions gϵM of the Levi form Gθ, such that the norm of the Reeb vector field T of (M, θ) is ...
Elisabetta Barletta +2 more
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Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry [PDF]
Advanced Nonlinear Studies, 2022 In this article, we establish a Gaffney type inequality, in Wℓ,p{W}^{\ell ,p}-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds)
Baldi Annalisa +2 more
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On geometry of sub-Riemannian η-Einstein manifolds
Дифференциальная геометрия многообразий фигур, 2019 On a sub-Riemannian manifold of contact type a connection with torsion is considered, called in the work a Ψ-connection. A Ψ-connection is a particular case of an N-connection.
S. Galaev
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Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion [PDF]
ESAIM: Proceedings and Surveys, 2018 In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit the information
Boscain Ugo +4 more
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On the Hausdorff volume in sub-Riemannian geometry [PDF]
, 2011 For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous
A. Agrachev +30 more
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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 ...
Ugo Boscain, Robert Neel, Luca Rizzi
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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 ...
Erlend Grong, Anton Thalmaier
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Sub-Riemannian geometry and Lie groups. Part II. Curvature of metric spaces, coadjoint orbits and associated representations [PDF]
, 2004 This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups.
Buliga, Marius
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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
Witold Respondek
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On the geometry of sub-Riemannian manifolds equipped with a canonical quarter-symmetric connection
Дифференциальная геометрия многообразий фигур, 2023 In this article, a sub-Riemannian manifold of contact type is understood as a Riemannian manifold equipped with a regular distribution of codimension-one and by a unit structure vector field orthogonal to this distribution. This vector field is called a
S. V. Galaev
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