Results 1 to 10 of about 33,123 (219)
A Formula for Popp’s Volume in Sub-Riemannian Geometry [PDF]
Analysis and Geometry in Metric Spaces, 2013 Abstract For an equiregular sub-Riemannian manifold M, Popp’s volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp’s volume, written in terms of a frame adapted to the sub-Riemannian ...
Barilari Davide, Rizzi Luca
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A connection theoretic approach to sub-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2003 We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism.
Bavo Langerock
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Sub-Riemannian geometry of the coefficients of univalent functions [PDF]
Journal of Functional Analysis, 2006 We consider coefficient bodies $\mathcal M_n$ for univalent functions. Based on the L\"owner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a representation of ...
Irina Markina +2 more
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Surface measure on, and the local geometry of, sub-Riemannian manifolds. [PDF]
Calc Var Partial Differ Equ, 2023 AbstractWe prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for the uniform convergence of parametrized sub-Riemannian distances, and local uniform asymptotics for the diameter of small metric balls.
Don S, Magnani V.
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Control of Nonholonomic Systems and Sub-Riemannian Geometry [PDF]
, 2012 Lectures given at the CIMPA School "Geometrie sous-riemannienne", Beirut, Lebanon ...
Frédéric Jean
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On the Hausdorff volume in sub-Riemannian geometry [PDF]
Calculus of Variations and Partial Differential Equations, 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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Characteristic Laplacian in sub-Riemannian geometry [PDF]
International Mathematics Research Notices, 2013 We study a Laplacian operator related to the characteristic cohomology of a smooth manifold endowed with a distribution. We prove that this Laplacian does not behave very well: it is not hypoelliptic in general and does not respect the bigrading on forms
Daniel, Jeremy, Ma, Xiaonan
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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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Sub-Riemannian geometry on infinite-dimensional manifolds [PDF]
The Journal of Geometric Analysis, 2012 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.
Erlend Grong +2 more
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Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry [PDF]
, 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 W. Neel, Luca Rizzi
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