Results 51 to 60 of about 33,123 (219)

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
doaj   +1 more source

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

Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds [PDF]

, 2015
We study eigenvalue problems for intrinsic sub-Laplacians on regular sub-Riemannian manifolds. We prove upper bounds for sub-Laplacian eigenvalues λk of conformal sub-Riemannian metrics that are asymptotically sharp as k→+∞. For Sasakian manifolds with a
Hassannezhad, A, Kokarev, G
core   +3 more sources

Homogeneous geodesics in sub-Riemannian geometry

ESAIM: Control, Optimisation and Calculus of Variations, 2023
We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic to be homogeneous in terms of its initial momentum. We prove that any weakly commutative sub-Riemannian homogeneous space is geodesic orbit, that means all geodesics are ...
openaire   +2 more sources

A New Subject-Specific Discriminative and Multi-Scale Filter Bank Tangent Space Mapping Method for Recognition of Multiclass Motor Imagery

Frontiers in Human Neuroscience, 2021
Objective: Tangent Space Mapping (TSM) using the geometric structure of the covariance matrices is an effective method to recognize multiclass motor imagery (MI).
Fan Wu, Fan Wu, Anmin Gong, Hongyun Li, Hongyun Li, Lei Zhao, Lei Zhao, Wei Zhang, Yunfa Fu, Yunfa Fu, Yunfa Fu, Yunfa Fu   +11 more
doaj   +1 more source

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
doaj   +1 more source

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.
openaire   +3 more sources

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
core   +2 more sources

Sard property in Carnot groups [PDF]

, 2021
In this work we introduce the topic of sub-Riemannian geometry from an elementary viewpoint. Sub-Riemannian geometry is a quite modern field of differential geometry.
Nalon, Luca
core   +1 more source

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source