Results 31 to 40 of about 732 (169)
On the Subelliptic Eikonal Equation
Bruno Pini Mathematical Analysis Seminar, 2017 On a bounded smooth domain, we consider the viscosity solution of the homogeneous Dirichlet problem for the eikonal equation associated with a system of Hörmander’s vector fields.
Paolo Albano
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An Inverse Problem from sub-Riemannian geometry [PDF]
Pacific Journal of Mathematics, 2003 The geodesics for a sub-Riemannian metric on a three-dimensional contact manifold $M$ form a 1-parameter family of curves along each contact direction. However, a collection of such contact curves on $M$, locally equivalent to the solutions of a fourth-order ODE, are the geodesics of a sub-Riemannian metric only if a sequence of invariants vanish.
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On the role of abnormal minimizers in sub-riemannian geometry [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 2001 Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^ω)$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.
Bonnard, Bernard, Trélat, Emmanuel
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Model spaces in sub-Riemannian geometry [PDF]
Communications in Analysis and Geometry, 2021 25 pages.
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How smooth is quantum complexity?
Journal of High Energy Physics, 2021 The “quantum complexity” of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational ...
Vir B. Bulchandani, S. L. Sondhi
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Liouville Integrability in a Four-Dimensional Model of the Visual Cortex
Journal of Imaging, 2021 We consider a natural extension of the Petitot–Citti–Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taken into account.
Ivan Galyaev, Alexey Mashtakov
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A proof of a trace formula by Richard Melrose
Advanced Nonlinear Studies, 2023 The goal of this article is to give a new proof of the wave trace formula proved by Richard Melrose in an impressive article. This trace formula is an extension of the Chazarain-Duistermaat-Guillemin trace formula (denoted as “CDG trace formula” in this ...
Colin de Verdière Yves
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Curvature and the equivalence problem in sub-Riemannian geometry
Archivum Mathematicum, 2022 These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with ...
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Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion
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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Journal of Differential Geometry, 1986 A sub-Riemannian or singular Riemannian geometry is given by a smoothly varying positive definite quadratic form defined only on a subbundle \(S\) of the tangent bundle \(TM\) of a differentiable manifold, \(S\) being bracket-generating, that is sections of \(S\) together with their Lie brackets generate the \(C^{\infty}(M)\)-module \(V(M)\) of vector ...
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