Géométrie Riemannienne
et analyse géométrique
Analyse non linéaire sur les
variétés
Equations aux dérivées partielles
Physique mathématique
Adresse:
Email:
hebey(at)u-cergy.fr , or
Emmanuel.Hebey(at)u-cergy.fr
WebPage: hebey.u-cergy.fr
Curriculum Vitae
Publications
Curriculum Vitae et Liste de Publications.
Fichier téléchargeable: pdf
| Emmanuel Hebey. Professor
of mathematics. Research interests in Partial Differential Equations and the Calculus of Variations, Geometric Analysis, and Differential Geometry. Born on april 10, 1964 at Paris, France. Studies at the University of Paris 6. PhD in 1990 and «habilitation à diriger des recherches» in 1991. Associate professor at the University of Paris 6 from 1990 to 1993. Full professor at the University of Cergy-Pontoise since 1993. Awarded the «Marie Guido Triossi» price of the French Academy of Sciences in 1995. Director of the math department (1994-1997). Director of the math research lab (1997-2004 and from 2015). Member of the scientific board of the university (2008-2016). Editorial boards: International Journal of Differential Equations, International Mathematics Research Notices (principal editor), Potential Analysis. PHD Students: Marie Dellinger, Zindine Djadli, Olivier Druet, Antoinette Jourdain, Benoit Pausader, Bruno Premoselli, Frédéric Robert, Nicolas Saintier, Pierre-Damien Thizy, Jérôme Vétois. |
| Monographies de
recherche: (Some research monographs)  [1] Nonlinear analysis on manifolds: Sobolev spaces and inequalities, CIMS Lecture Notes, Courant Institute of Mathematical Sciences, New York University, Volume 5, 1999. Seconde édition publiée conjointement avec l'American Mathematical Society, 290 pages, AMS/CIMS Lecture Notes , Volume 5, 2000. Version traduite en russe, Editions Tamara Rozhkovskaya, 2008. [2] The AB program in Geometric Analysis. Sharp Sobolev inequalities and related problems, Memoirs of the American Mathematical Society , avec O.Druet, 98 pages, MEMO/160/761, 2002. [3] Blow-up theory for elliptic PDEs in Riemannian geometry, Mathematical Notes , Princeton University Press, avec O.Druet et F.Robert, 218 pages, Volume 45, 2004. [4] Elliptic equations of Yamabe type, avec O.Druet, International Mathematics Research Surveys, IMRS, Issue 1, 1-113, 2005. [5] Compactness and stability for nonlinear elliptic equations, Zurich Lectures in Advanced Mathematics, ZLAM, 291 pages, European Mathematical Society, Volume 20, 2014. |
| Textes
en libre service: (Unpublished texts with free access) [1] Sharp Sobolev-Poincaré inequalities on compact Riemannian manifolds, NotesSharpSP.pdf , 121 pages, 2002. Contains unpublished results. [2] Variational methods and elliptic equations in Riemannian geometry, Notes from lectures given at ICTP, NotesICTP.pdf , 63 pages, 2003. [3] Manifolds which are close to space forms and the Bemelmans, Min-Oo and Ruh smoothing effect of the Ricci flow, NotesSF.pdf , 5 pages, 2002. Unpublished results. [4] An introduction to fourth order nonlinear wave equations, avec B.Pausader, FourthOrderWaves.pdf , 48 pages, 2008. Contains unpublished results. [5] Existence, stability and instability for Einstein-scalar field Lichnerowicz equations, EinLich.pdf, Slides, Contains unpublished results, 46 pages, 2008/2009. [6] Super critical energy scale invariant equations in critical spaces, SuperCrit.pdf, 6 pages, 2010. Rewriting of a known result. [7] Elliptic stability for stationary Schrödinger equations, Part I, PartII, and PartIII. Slides from a three parts course given in 2013. [8] Companion tables for the above slides on elliptic stability, Tables, 2013. [9] Elliptic stability for stationary Schrödinger equations, Part I, Part II, Part III, Part IV, Part V, Part VI. Slides (extended version) of a course given in 2015. [10] Klein-Gordon-Maxwell-Proca systems in closed manifolds, KGMPSlides, Slides from a talk, 37 pages, 2014. [11] Nonnegative solutions of stationary Kirchhoff systems, KirchhoffSyst, Slides from a talk, 30 pages, 2015. |
| Quelques articles
récents: (Some recent research papers) [1] Bounded stability for strongly coupled critical elliptic systems below the geometric threshold of the conformal laplacian, avec O. Druet et J.Vétois, Journal of Functional Analysis, 258, 999–1059, 2010. [2] The Lin-Ni's conjecture for vector valued Schrödinger equations in the closed case, Communications in Pure and Applied Analysis, 9, 955–962, 2010. [3] Existence and a priori bounds for Klein-Gordon-Maxwell systems in fully inhomogeneous spaces, avec O. Druet, Communications in Contemporary Mathematics, 12, 831–869, 2010. [4] Asymptotic analysis for fourth order Paneitz equations with critical growth, avec F.Robert, Advances in the Calculus of Variations, 3, 229–276, 2011. [5] Static Klein-Gordon-Maxwell-Proca systems in 4-dimensional closed manifolds, avec T.T.Truong, Journal für di reine und angewandte Mathematik (Crelle's journal), 667, 221-248, 2012. [6] Solitary waves in critical Abelian gauge theories, Discrete and Continuous Dynamical Systems - Series A, 32, 1747–1761, 2012. [7] Resonant states for the static Klein-Gordon-Maxwell-Proca system, avec J.Wei, Mathematical Research Letters, 19, 4, 953–967, 2012. [8] Schrödinger-Poisson systems in the 3-sphere, avec J.Wei, 33 pages, Calculus of Variations and Partial Differential Equations, 47, 25-54, 2013. [9] Stability of elliptic PDEs with respect to perturbations of the domain, avec O.Druet et P.Laurain, Journal of Differential Equations, 10, 3703–3718, 2013. [10] The Lichnerowicz equation in the closed case of the Einstein-Maxwell theory, avec G.Veronelli, Transactions of the American Mathematical Society, 366, 1179–1193, 2014. [11] Stationary Kirchhoff systems in closed 3-dimensional manifolds, avec P.D.Thizy, Calculus of Variations and Partial Differential Equations, 54, 2085-2114, 2015. [12] Static Klein-Gordon-Maxwell-Proca systems in 4-dimensional closed manifolds. II, avec O.Druet et J.Vétois, Journal für di reine und angewandte Mathematik (Crelle's journal), 713, 149-179, 2016. [13] Stationary Kirchhoff systems in closed high dimensional manifolds, avec P.D.Thizy, Communications in Contemporary Mathematics, 18, Issue 02, 1550028 (53 pages), 2016. [14] Compactness and the Palais-Smale property for critical Kirchhoff equations in closed manifolds, Pacific Journal of Mathematics, 280, 41-50, 2016. [15] Multiplicity of solutions for critical Kirchhoff type equations, 12 pages, Communications in Partial Differential Equations, à paraître. [16] Stationary Kirchhoff equations with powers, 29 pages, Advances in the Calculus of Variations, à paraître. [17] Klein-Gordon-Maxwell-Proca type systems in the electro-magneto-static case, avec P.D.Thizy, 36 pages, Preprint. |
Des Liens:
Séminaire Géométrie, EDP et Physique Mathématique
Arxiv Maths
L'université de Cergy-Pontoise
Le laboratoire d'analyse, géométrie et modélisation
La
Société
Mathématique de France
L'American Mathematical
Society
L'European Mathematical Society
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mathworld
Mise à jour: Juin 2017