Ludovic Rifford

Preprints · Papers · Monographs · Proceedings · Theses

Preprints

(with André Belotto da Silva and Adam Parusinski) Abnormal subanalytic distributions and minimal rank Sard Conjecture
72 pages, 2022
(with André Belotto da Silva and Adam Parusinski) Abnormal singular foliations and the Sard Conjecture for generic co-rank one distributions
28 pages, 2023

Papers

Subdifferentials and Minimizing Sard Conjecture in Sub-Riemannian Geometry
Journal de l'École Polytechnique, vol. 10, 1195-1244, 2023
On the time for a runner to get lonely
Acta Applicandae Mathematicae, vol. 180, Paper No. 15, 66 pp., 2022
(with André Belotto da Silva, Alessio Figalli and Adam Parusinski) Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3
Inventiones Mathematicae, vol. 229(1), 395-448, 2022
A Quantitative version of Tao's result on the Toeplitz Square Peg Problem
North-Western European Journal of Mathematics, vol. 8, 61-90, 2022
(with Rafael Ruggiero) On the stability conjecture for geodesic flows of manifolds without conjugate points
Annales Henri Lebesgue, vol. 4, 759-784, 2021
(with Zeinab Badreddine) Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups
Annales de l'Institut Fourier (Grenoble), vol. 70(6), 2303-2330, 2020
(with Abbas Moameni) Uniquely minimizing costs for the Kantorovitch problem
Annales de la Faculté des Sciences de Toulouse, vol. 29(3), 507-563, 2020
(with André Belotto da Silva) The Sard conjecture on Martinet surfaces
Duke Mathematical Journal, vol. 167(8), 1433-1471, 2018
(with Aris Daniilidis, Robert Deville and Estibalitz Durand-Cartagena) Self-contracted curves in Riemannian manifolds
Journal of Mathematical Analysis and Applications, vol. 457(2), 1333-1352, 2018
(with Ayadi Lazrag and Rafael Ruggiero) Franks' lemma for C2-Mañé perturbations of Riemannian metrics and application to persistence
Journal of Modern Dynamics, vol. 10, 379-411, 2016
(with Luc Barbet, Marc Dambrine and Aris Daniilidis) Sard theorems for Lipschitz functions and applications in Optimization
Israel Journal of Mathematics, vol. 212(2), 757-790, 2016
(with Robert McCann) The intrisic dynamics of optimal transport
Journal de l'École Polytechnique, vol. 3, 67-98, 2016
(with Alessio Figalli and Thomas Gallouet) On the convexity of injectivity domains on nonfocal manifolds
SIAM Journal on Mathematical Analysis, vol. 47(2), 969-1000, 2015
(with Gonzalo Contreras and Alessio Figalli) Generic hyperbolicity of Aubry sets on surfaces
Inventiones Mathematicae, vol. 200(1), 201-261, 2015
(with Alessio Figalli) Closing Aubry sets II
Communications on Pure and Applied Mathematics, vol. 68(3), 345-412, 2015
(with Alessio Figalli) Closing Aubry sets I
Communications on Pure and Applied Mathematics, vol. 68(2), 210-285, 2015
Ricci curvatures in Carnot groups
Mathematical Control and Related Fields, vol. 3(4), 467-487, 2013
Closing geodesics in C1 topology
Journal of Differential Geometry, vol. 91(3), 361-382, 2012
(with Rafael Ruggiero) Generic properties of closed orbits of Hamiltonian flows from Mañé's viewpoint
International Mathematics Research Notices, vol. 22, 5246-5265, 2012
(with Alessio Figalli and Cédric Villani) Nearly round spheres look convex
American Journal of Mathematics, vol. 134(1), 109-139, 2012
(with Alessio Figalli and Cédric Villani) Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds
Tohoku Mathematical Journal, vol. 63(4), 855-876, 2011
(with Alessio Figalli and Cédric Villani) Tangent cut loci on surfaces
Differential Geometry and its Applications, vol. 29(2), 154-159, 2011
(with Ahed Hindawi and Jean-Baptiste Pomet) Mass transportation with LQ cost functions
Acta Applicandae Mathematicae, vol. 113(2), 215-229, 2011
(with Bernard Bonnard and Jean-Baptiste Caillau) Convexity of injectivity domains on the ellipsoid of revolution: The oblate case
Comptes Rendus de l'Académie des Sciences de Paris, vol. 348(23-24), 1315-1318, 2010
(with Alessio Figalli and Cédric Villani) On the Ma-Trudinger-Wang curvature on surfaces
Calculus of Variations and Partial Differential Equations, vol. 39(3-4), 307-332, 2010
(with Marco Castelpietra) Regularity properties of the distance function to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry
ESAIM - Control, Optimization and Calculus of Variations, vol. 16(3), 695-718, 2010
(with Alessio Figalli) Mass Transportation on sub-Riemannian Manifolds
Geometric and Functional Analysis, vol. 20(1), 124-159, 2010
(with Alessio Figalli) Continuity of optimal transport maps and convexity of injectivity domains on small deformations of the two-sphere
Communications on Pure and Applied Mathematics, vol. 62(12), 1670-1706, 2009
(with Albert Fathi and Alessio Figalli) On the Hausdorff Dimension of the Mather Quotient
Communications on Pure and Applied Mathematics, vol. 62(4), 445-500, 2009
(with Emmanuel Trélat) On the stabilization problem for nonholonomic distributions
Journal of the European Mathematical Society, vol. 11(2), 223-255, 2009
(with Piermarco Cannarsa) Semiconcavity results for optimal control problems admitting no singular minimizing controls
Annales de l'Institut Henri Poincaré Analyse Non Linéaire, vol. 25(4), 773-802, 2008
On viscosity solutions of certain Hamilton-Jacobi equations: Regularity results and generalized Sard's Theorems
Communications in Partial Differential Equations, vol. 33(3), 517-559, 2008
Erratum
Refinement of the Benoist Theorem on the size of Dini subdifferentials
Communications in Pure and Applied Analysis, vol. 7(1), 119-124, 2008
On the existence of local smooth repulsive stabilizing feedbacks in dimension three
Journal of Differential Equations, vol. 226(2), 429-500, 2006
À propos des sphères sous-riemanniennes
Bulletin of the Belgian Mathematical Society Simon Stevin, vol. 13(3), 521-526, 2006
(with Marc-Olivier Czarnecki) Approximation and regularization of Lipschitz functions: convergence of the gradients
Transactions of the American Mathematical Society, vol. 358(10), 4467-4520, 2006
(with Emmanuel Trélat) Morse-Sard type results in sub-Riemannian geometry
Mathematische Annalen, vol. 332(1), 145-159, 2005
Stratified semiconcave control-Lyapunov functions and the stabilization problem
Annales de l'Institut Henri Poincaré Analyse Non Linéaire, vol. 22(3), 343-384, 2005
A Morse-Sard theorem for the distance function on Riemannian manifolds
Manuscripta Mathematica, vol. 113, 251-265, 2004
(with Michael Malisoff and Eduardo D. Sontag) Global asymptotic controllability implies input to state stability
SIAM Journal of Control and Optimization, vol. 42(6), 2221-2238, 2004
Range of the gradient of a smooth bump function in finite dimensions
Proceedings of the American Mathematical Society, vol. 131(10), 3063-3066, 2003
Singularities of viscosity solutions and the stabilization problem in the plane
Indiana University Mathematical Journal, vol. 52(5), 1373-1396, 2003
Semiconcave control-Lyapunov functions and stabilizing feedbacks
SIAM Journal of Control and Optimization, vol. 41(3), 659-681, 2002
(with Francis H. Clarke and Ronald J. Stern) Feedback in state constrained optimal control
ESAIM - Control, Optimization and Calculus of Variations, vol. 7, 97-133, 2002
On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients
ESAIM - Control, Optimization and Calculus of Variations, vol. 6, 593-611, 2001
Existence of Lipschitz and semiconcave control-Lyapunov functions
SIAM Journal of Control and Optimization, vol. 39(4), 1043-1064, 2000
(with Francis H. Clarke, Yuri S. Ledyaev and Ronald J. Stern) Feedback stabilization and Lyapunov functions
SIAM Journal of Control and Optimization, vol. 39(1), 25-48, 2000
Stabilisation des systèmes globalement asymptotiquement commandables
Comptes Rendus de l'Académie des Sciences de Paris, vol. 330(3), 211-216, 2000

Monographs

Sub-Riemannian Geometry and Optimal Transport
SpringerBriefs in Mathematics, 2014

Proceedings

Quelques propriétés des champs de vecteurs génériques
In Informatique Mathématique Une photographie en 2022, Chapitre 4, 91-115, 2022
Singulières minimisantes en géométrie sous-riemannienne [d'après Hakavuori, Le Donne, Leonardi, Monti...]
In Séminaire Bourbaki, Vol. 2015/2016. Exposés 1104-1119. Astérisque, No. 390, Exp. No. 113, 277-301, 2017
(with Alessio Figalli) Aubry sets, Hamilton-Jacobi equations, and Mañé Conjecture
In Geometric Analysis, Mathematical Relativity, and Nonlinear Partial Differential Equations, Contemp. Math., 599, Amer. Math. Soc., Providence, RI, 2013
Regularity of weak KAM solutions and Mañé's Conjecture
In Séminaire Laurent Schwartz - EDP et applications (2011-2012):1-22
Stabilization problem for nonholonomic control systems
In Geometric Control and Nonsmooth Analysis, Series on Advances in Mathematics for Applied Sciences Vol. 76, World Scientific, pp. 260-269, 2008
The stabilization problem on surfaces
Rendiconti des Seminario Matematico, università e Politecnico Torino, Control Theory and Stabilization II, 64(1):55-61, 2006
The stabilization problem: AGAS and SRS feedbacks
In Optimal Control, Stabilization, and Nonsmooth Analysis, Lectures Notes in Control and Information Sciences Vol. 301, Springer-Verlag, Heidelberg, 2004, pp. 173-184
(with Michael Malisoff and Eduardo D. Sontag) Remark on input to state stabilization
In Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, December 2003
(with Alain Rapaport) Stabilization of the logistic law under yield control constrained to initial harvest
In Proceedings of the 4th European Control Conference, Brussels, July 1997

Theses

Problème de Stabilisation et Géométrie Sous-Riemannienne
Habilitation à diriger des recherches, Université de Paris-Sud, 2005
Problèmes de stabilisation en théorie du contrôle
PhD Thesis, Université Claude Bernard Lyon I, 2000

	Ludovic Rifford, Laboratoire J.A. Dieudonné, Université Côte d'Azur, Parc Valrose, 06108 Nice Cedex 2, France
	+33 4 89 15 06 34
	ludovic.rifford@math.cnrs.fr