Works in progress:
L. Rifford, Nonholonomic Variations: An Introduction to Sub-Riemannian Geometry.
A. Figalli, T. Gallouet, L. Rifford, Ma-Trudinger-Wang condition vs. Convexity of injectivity domains.
M. Malisoff, L. Rifford, A Jurdjevic-Quinn Theorem on compact manifolds.
L. Rifford, Generalized Ricci curvatures on generic Carnot groups.
A. Figalli, L. Rifford, Closing Aubry sets I, 65 pages. pdf
A. Figalli, L. Rifford, Closing Aubry sets II, 58 pages. pdf
L. Rifford, Closing geodesics in C1 topology, J. Differential Geom., 23 pages, to appear. pdf
L. Rifford, R. Ruggiero, Generic properties of closed orbits of Hamiltonian flows from Mañé's viewpoint, Int. Math. Res. Not.,18 pages, to appear. 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
Proceedings:
L. Rifford, Regularity of weak KAM solutions and Mañé's Conjecture, in Séminaire Équations aux dérivées partielles (Polytechnique), 22 pages, to appear. 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
Talks:
A Kupka-Smale Theorem for Hamiltonian systems from Mañé's viewpoint, a control approach, in PICOF 2012, Ecole Polytechnique, 2012. pdf
Transport de masse sur la Terre, in Colloque 2012 de la Société Mathématique de Tunisie, 2012. pdf
Mass Transportation on the Earth, University of the Basque Country, 2012. pdf
Transport de masse sur la Terre, Colloquium de l'Institut de Mathématiques de Jussieu, 2012. pdf
Transport de masse sur les surfaces, Université Paris-Sud XI, 2011. pdf
Mass Transportation on the Earth, in Geometry Meets Transport, Université de Nice, 2011. pdf
Geometric control theory, closing lemma, and weak KAM theory (4 lectures), in Weak KAM Theory in Italy, Cortona (Italy), 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, 2011. pdf
Perspectives sous-riemanniennes, Université Paris-Sud XI, 2011. pdf
Premiers pas vers la conjecture de Mañé en topologie C2, Université Paris VI, 2011. pdf
Sur les variétés riemanniennes jouissant de bons transports optimaux, Universités de Grenoble, Cergy-Pontoise, Toulouse, 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, 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, 2010. pdf
On Riemannian manifolds satisfying the Transport Continuity Property, in Recent Advances Optimal Transportation and Applications, Université de Nice, 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, 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