Results 41 to 50 of about 33,779 (212)

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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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, A. Agrachev, A. Bonfiglioli, A.A. Agrachev, A.A. Agrachev, A.A. Agrachev, A.A. Agrachev, Andrei Agrachev, B. Franchi, Davide Barilari, F. Jean, H. Federer, I. Chavel, J. Mitchell, J.-P. Gauthier, J.-P. Gauthier, J.-P. Gauthier, L. Ambrosio, L. Ambrosio, L. Capogna, L.P. Rothschild, P. Rashevsky, R. Montgomery, R. Monti, R.M. Bianchini, T. Kato, Ugo Boscain, V. Jurdjevic, W.-L. Chow, Z.M. Balogh, Z.M. Balogh   +30 more
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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
doaj   +1 more source

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

, 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
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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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The rolling problem: overview and challenges

, 2012
In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the ...
A Agrachev, A Agrachev, A Agrachev, A Chelouah, A Marigo, A Marigo, AM Bloch, AV Borisov, Cartan, Cartan, DJ Montana, DW Stroock, E Grong, EP Hsu, F Alouges, G Bor, H Sussmann, I Zelenko, I Zelenko, IM Singer, J Zimmerman, J-M Bismut, K Hüper, K Hüper, K Nomizu, M Godoy Molina, M Godoy Molina, P Rouchon, PB Gilkey, PE Jupp, R Bryant, R Montgomery, R Murray, RW Sharpe, S Kobayashi, SA Chaplygin, SA Chaplygin, T Sakai, V Jurdjevic, V Jurdjevic, V Jurdjevic, Y Chitour, Y Chitour, Y Chitour, Z Li   +44 more
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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   +3 more sources

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, Chertovskih Roman, Gauthier Jean-Paul, Prandi Dario, Remizov Alexey   +4 more
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Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D [PDF]

, 2017
We propose an efficient approach for the grouping of local orientations (points on vessels) via nilpotent approximations of sub-Riemannian distances in the 2D and 3D roto-translation groups $SE(2)$ and $SE(3)$.
Bekkers, Erik J., Chen, Da, Portegies, Jorg M.   +2 more
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