Dieudonné Laboratory research group
Algebra, Geometry and Topology
ANR projects Sub-Riemannian Geométry
and Interactions (SRGI), Intéractions
Systèmes Dynamiques Équations
d'Évolution et Contrôle (ISDEEC)
A. Belotto da Silva, A. Figalli, A. Parusinski, L. Rifford, Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3, 37 pages. pdf
L. Rifford, R. Ruggiero, On the stability conjecture for geodesic flows of manifolds without conjugate points, 19 pages. pdf
Z. Badreddine, L. Rifford, Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups, 24 pages. pdf
A. Moameni, L. Rifford, Uniquely minimizing costs for the Kantorovitch problem. Ann. Fac. Sci. Toulouse Math., to appear. pdf
A. Belotto da Silva, L. Rifford, The Sard conjecture on Martinet surfaces. Duke Math. J., 167(8):1433-1471, 2018. pdf
A. Daniilidis, R. Deville, E. Durand-Cartagena, L. Rifford, Self-contracted curves in Riemannian manifolds, J. Math. Anal. Appl., 457(2):1333-1352, 2018. pdf
A. Lazrag, L. Rifford, R. Ruggiero, Franks'
lemma
for C2-Mañé perturbations of Riemannian metrics and application to
persistence, J.
Mod. Dyn., 10:379-411, 2016. pdf
L. Barbet, M. Dambrine, A. Daniilidis, L. Rifford, Sard theorems for Lipschitz functions and applications in Optimization, Israel J. Math., 212(2):757-790, 2016. pdf
R.J. McCann, L. Rifford, The intrisic dynamics of optimal transport, J. Éc. polytech. Math., 3:67-98, 2016. pdf
A. Figalli, T. Gallouet, L. Rifford, On the convexity of injectivity domains on nonfocal manifolds, SIAM J. Math. Anal., 47(2):969-1000, 2015. pdf
G. Contreras, A. Figalli, L. Rifford, Generic hyperbolicity of Aubry sets on surfaces, Invent. Math., 200(1):201-261, 2015. pdf
A. Figalli, L. Rifford, Closing Aubry sets II, Comm. Pure Appl. Math., 68(3):345-412, 2015. pdf
A. Figalli, L. Rifford, Closing Aubry sets I, Comm. Pure Appl. Math., 68(2):210-285, 2015. pdf
L. Rifford, Ricci curvatures in Carnot groups, Math. Control Relat. Fields, 3(4):467-487, 2013. pdf
L. Rifford, Closing geodesics in C1 topology, J. Differential Geom., 91(3):361-382, 2012. pdf
L. Rifford, R. Ruggiero, Generic properties of closed orbits of Hamiltonian flows from Mañé's viewpoint, Int. Math. Res. Not., 22:5246-5265, 2012. pdf
A. Figalli, L. Rifford, C. Villani, Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds, Tohoku. Math. J., 63(4):855-876, 2011. pdf
A. Figalli, L. Rifford, C. Villani, Tangent cut loci on surfaces, Differential Geom. Appl., 29(2):154-159, 2011. pdf
A. Hindawi, L. Rifford, J.-B. Pomet, Mass transportation with LQ cost functions, Acta Appl. Math., 113(2):215-229; 2011. pdf
B. Bonnard, J.-B. Caillau, L. Rifford, Convexity of injectivity domains on the ellipsoid of revolution: The oblate case, C. R. Acad. Sci. Paris Sér. I Math., 348(23-24):1315-1318, 2010. pdf
A. Figalli, L. Rifford, C. Villani, On the Ma-Trudinger-Wang curvature on surfaces, Calc. Var. Partial Differential Equations, 39(3-4):307-332, 2010. pdf
M. Castelpietra, L. Rifford, 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 Optim. Calc. Var., 16(3):695-718, 2010. pdf
A. Figalli, L. Rifford, Mass Transportation on sub-Riemannian Manifolds, Geom. Funct. Anal., 20(1):124-159, 2010. pdf
L. Rifford, E. Trélat, On the stabilization problem for nonholonomic distributions, J. Eur. Math. Soc., 11(2):223-255, 2009. pdf
A. Fathi, A. Figalli, L. Rifford, On the Hausdorff Dimension of the Mather Quotient, Comm. Pure Appl. Math., 62(4):445-500, 2009. pdf
P. Cannarsa, L. Rifford, Semiconcavity results for optimal control problems admitting no singular minimizing controls, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25(4):773-802, 2008. pdf
L. Rifford, On viscosity
solutions of certain Hamilton-Jacobi equations: Regularity results and
generalized Sard's Theorems, Comm.
Partial Differential Equations, 33(3):517-559, 2008. pdf
L. Rifford, A refinement of the Benoist Theorem on the size of Dini subdifferentials, Commun. Pure Appl. Anal., 7(1):119-124, 2008. pdf
L. Rifford, À propos des sphères sous-riemanniennes, Bull. Belg. Math. Soc. Simon Stevin, 13(3):521-526, 2006. pdf
M.-O. Czarnecki, L. Rifford, Approximation and regularization of Lipschitz functions : convergence of the gradients, Trans. Amer. Math. Soc., 358(10):4467-4520, 2006.
L. Rifford, On the existence of local smooth repulsive stabilizing feedbacks in dimension three, J. Differential Equations, 226(2):429-500, 2006. pdf
L. Rifford, E. Trélat, Morse-Sard type results in sub-Riemannian geometry, Math. Ann., 332(1):145-159, 2005. pdf
L. Rifford, Stratified semiconcave control-Lyapunov functions and the stabilization problem, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22(3):343-384, 2005. pdf
L. Rifford, A Morse-Sard theorem for the distance function on Riemannian manifolds, Manuscripta Math., 113:251-265, 2004. pdf
M. Malisoff, L. Rifford, E. D. Sontag, Asymptotic controllability implies input to state stability, SIAM J. Control Optim., 42(6):2221-2238, 2004. pdf
L. Rifford, Singularities of viscosity solutions and the stabilization problem in the plane, Indiana Univ. Math. J, 52(5):1373-1396, 2003. pdf
L. Rifford, Range of the gradient of a smooth bump function in finite dimensions, Proc. Amer. Math. Soc., 131(10):3063-3066, 2003. pdf
L. Rifford, Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM J. Control Optim., 41(3):659-681, 2002.
F. H. Clarke, L. Rifford, R. J. Stern, Feedback in state constrained optimal control, ESAIM Control Optim. Calc. Var., 7:97-133, 2002.
L. Rifford, On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients, ESAIM Control Optim. Calc. Var., 6:593-611, 2001. pdf
L. Rifford, Existence of Lipschitz and semiconcave control-Lyapunov functions, SIAM J. Control Optim., 39(4):1043-1064, 2000. pdf
F. H. Clarke, Yu. S. Ledyaev, L. Rifford, R. J. Stern, Feedback stabilization and Lyapunov functions, SIAM J. Control Optim., 39(1):25-48, 2000. pdf
Monographs:
L. Rifford, Sub-Riemannian
Geometry and Optimal Transport, Springerbriefs in
Mathematics, 2014. pdf
Proceedings:
L. Rifford, 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. pdf
A. Figalli, L. Rifford, 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. pdf
L. Rifford, Regularity of weak KAM solutions and Mañé's Conjecture, in Séminaire Laurent Schwartz - EDP et applications (2011-2012):1-22. pdf
L. Rifford, 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. pdf
L. Rifford, The stabilization problem on surfaces, Rend. Semin. Mat. Torino, Control Theory and Stabilization II, 64(1):55-61, 2006. pdf
L. Rifford, 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. pdf
M. Malisoff, L. Rifford, E. D. Sontag, Remark on input to state stabilization, in Proceedings of the 42nd IEEE Conference on Decision and Control (Maui, HI, December 2003),pp. 1053-1058. pdf
Lecture Series:
Introduction to Sub-Riemannian Geometry (2 lectures), Center for Mathematical Modelling, Santiago (Chile), 2015. pdf
Geometric control and weak applications (2 lectures), in Minischool on Variational problems in Geometry, Fields Institute, Toronto (Canada), 2014. pdf
Geometric control and sub-Riemannian geodesics (4 lectures), in Summer School CIRM "Sub-Riemannian manifolds: from geodesics to hypoelliptic diffusion, Marseille, 2014. pdf
Geometric control theory, closing lemma, and weak KAM theory (4 lectures), in Weak KAM Theory in Italy, Cortona (Italy), 2011. pdf
Talks:
Recent progress in sub-Riemannian geometry, in Second International Conference of Mathematics in Erbil, Salahaddin University (Iraq), 2019. pdf
Recent progress in sub-Riemannian geometry, in Dynamical Aspects in Variational Analysis, École Polytechnique (France), 2018. pdf
Sard conjecture and regularity of singular minimizing curves for sub-Riemannian structures in dimension three, in Géométrie Riemannienne et fonctions généralisées, Université Paris Diderot (France), 2018. pdf
The Sard conjectures and measure contraction properties in sub-Riemannian geometry, in Sub-Riemannian Geometry and Beyond, University of Jyväskylä (Finland), 2018. pdf
The Sard Conjecture on Martinet Surfaces, in Conference in honor of Ahmad El Soufi, Université François Rabelais, Tours (France), 2017. pdf
The Sard Conjecture on Martinet Surfaces, in New Trends in Control Theory and PDEs (in honor of Piermarco Cannarsa), INDAM, Rome (Italy), 2017. pdf
The Sard Conjecture on Martinet Surfaces, in Pan African Congress of Mathematicians 2017, Université Mohammed V, Rabat (Morocco), 2017. pdf
The cut locus in optimal transportation, in Conference "The cut locus", KMITL, Bangkok (Thailand), 2016. pdf
The intrinsic dynamics of optimal transport, in CMC Conference "Analysis, Geometry, and Optimal Transport", KIAS, Seoul (South Corea), 2016. pdf
La conjecture de Sard sous-riemannienne, Colloquium, Université Paris-Sud XI, Orsay (France), 2016. pdf
Courbes auto-contractantes dans les variétés riemanniennes, in Colloque International du Groupement Euro-Maghrébin de Mathématiques et de ses Interactions, Hammamet (Tunisia), 2016. pdf
Courbes auto-contractantes dans les variétés riemanniennes, in École CIMPA "Géométrie et Analyse", Université Félix Houphouët-Boigny, Abidjan (Ivory Coast), 2016. pdf
Courbes auto-contractantes dans les variétés riemanniennes, in Rencontre d'Analyse Mathématique et ses Applications, Ouargla (Algeria), 2016. pdf
Regularity of weak KAM solutions, in SIAM Conference on Analysis of Partial Differential Equations, Scottsdale (USA), 2015. pdf
The intrinsic dynamics of optimal transport, in Workshop Analysis in Lyon, ENS Lyon, Lyon (France), 2015. pdf
Regularity of solutions to Hamilton-Jacobi equations for Tonelli Hamiltonians, in Nonlinear Analysis and Optimization, Royal Society, London (UK), 2015. pdf
Mass Transportation on the Earth, Colloquium Department of Mathematics, PUC, Santiago (Chile), 2015. pdf
Franks' Lemma for Mañé perturbations of Riemannian metrics and applications, in Workshop on Hamiltonian dynamical systems, Fudan University, Shanghai (China), 2015. pdf
Control and Dynamics, in Analysis and Geometry in Control Theory and Applications, INDAM, Rome (Italy), 2014. pdf
A few words about the Ma-Trudinger-Wang tensor, in Salah Baouendi Memorial Conference, Mediterranean Institute for the Mathematical Sciences, Tunis (Tunisia), 2014. pdf
Regularity of optimal transport maps on Riemannian manifolds, in Recent Development of nonlinear PDE, Australian National , Canberra (Australia), 2013. pdf
Optimal Transport and Control, in Workshop on Control and Observation of Nonlinear Control Systems with Application to Medicine, University of Hawaii at Manoa, Honolulu (USA), 2013. pdf
Mass Transportation on the Earth, University of Sciences and Technology of China, Hefei (China), 2013. pdf
Generic Aubry sets on surfaces, Nanjing University, Nanjing (China), 2013. pdf
From the Poincaré "lignes de partage" to the convex earth theorem, in International Conference "Henri Poincaré : du mathématicien au philosophe", Institut Henri Poincaré, Paris (France), 2012. pdf
Geometric control and dynamical systems, in 9th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Orlando (USA), 2012. pdf
MTW condition vs. convexity of injectivity domains, in Contrôle optimal géométrique, Université de Bourgogne, Dijon (France), 2012. pdf
Mañé's Conjecture from the control viewpoint, in INDAM meeting on Geometric Control and sub-Riemannian Geometry, Cortona (Italy), 2012. pdf
A Kupka-Smale Theorem for Hamiltonian systems from Mañé's viewpoint, a control approach, in PICOF 2012, École Polytechnique, Palaiseau (France), 2012. pdf
Transport de masse sur la Terre, in Colloque 2012 de la Société Mathématique de Tunisie, Mahdia (Tunisia), 2012. pdf
Mass Transportation on the Earth, University of the Basque Country, Bilbao (Spain) 2012. pdf
Transport de masse sur la Terre, Colloquium de l'Institut de Mathématiques de Jussieu, Paris (France), 2012. pdf
Transport de masse sur les surfaces, Université Paris-Sud XI, Orsay (France), 2011. pdf
Mass Transportation on the Earth, in Geometry Meets Transport, Université Nice Sophia Antipolis, Nice (France), 2011. pdf
Stabilization of finite-dimensional control systems: a survey, in OPTDE - Summer School, Basque Center for Applied Mathematics, Bilbao (Spain), 2011. pdf
Mass transportation on surfaces, in Nonlinear PDEs Workshop, Instituto Superior Técnico, Lisbon (Portugal), 2011. pdf
Transport de masse sur les surfaces, Colloquium Lorrain de Mathématiques, Université de Nancy, Nancy (France), 2011. pdf
Perspectives sous-riemanniennes, Université Paris-Sud XI, Orsay (France), 2011. pdf
Premiers pas vers la conjecture de Mañé en topologie C2, Université Paris VI, Paris (France), 2011. pdf
Sur les variétés riemanniennes jouissant de bons transports optimaux, Universités de Grenoble, Cergy-Pontoise, Toulouse, France, 2010-2011. pdf
Nearly round spheres look convex, in Workshop on Optimal Transportation and Applications, SNS Pisa (Italy), 2010. pdf
Optimal Transport on Surfaces, in Topics on Optimal Transport, Strasbourg (France), 2010. pdf
On Riemannian manifolds satisfying the Transport Continuity Property, in Optimal Transportation and Applications, Banff (Canada), 2010. pdf
Generic regularity of weak KAM solutions and Mañé conjecture, in Nonlinear Analysis and PDEs, University of Texas at Austin (USA), 2010. pdf
Sur les variétés riemanniennes jouissant de bons transports optimaux, Université d'Orléans, Orléans (France), 2010. pdf
On Riemannian manifolds satisfying the Transport Continuity Property, in Recent Advances Optimal Transportation and Applications, Université Nice Sophia Antipolis, Nice (France), 2009. pdf
Optimal Transportation on Sub-Riemannian Manifolds, in Optimal Transportations and Applications, SNS Pisa (Italy), 2008. pdf
Optimal Transportation on Sub-Riemannian Manifolds, in 50 Years of Optimal Control, Banach Center, Bedlewo (Poland), 2008. pdf
On the Mather Quotient, in Atelier sur les aspects de la mécanique céleste, Institut Henri Poincaré, Paris (France), 2007. pdf
PhD
Thesis:
Problèmes de stabilisation en théorie du contrôle. Thèse soutenue le 11 mai 2000 à l'Université Claude Bernard Lyon I, Mention très honorable avec félicitations. Jury : H. Attouch (président), J.-B. Hiriart-Urruty, E.D. Sontag, R. Vinter (rapporteurs), J.-B. Baillon, J. Blum, F. Clarke, J.-M. Coron (examinateurs). pdf
Habilitation à diriger des recherches:
Problème de Stabilisation et Géométrie Sous-Riemannienne. Soutenue le 24 octobre 2005 à l'Université de Paris-Sud. Jury : H. Attouch (président), B. Bonnard, A. Bressan, J.-M. Coron (rapporteurs), F. Clarke, A. Fathi, P. Pansu (examinateurs). pdf