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Emmanuel Hebey
Professeur des universitésEH2020

Géométrie Riemannienne et analyse géométrique
Analyse non linéaire sur les variétés
Equations aux dérivées partielles
Physique mathématique

Cours ETH 2012Adresse:
Université de Cergy-Pontoise
Département de Mathématiques
2 avenue Adolphe Chauvin
95302 Cergy-Pontoise cedex


WebPage: hebey.u-cergy.fr

Curriculum Vitae

Curriculum Vitae et Liste de Publications.
Fichier téléchargeable:  pdf

Poster A quoi servent les mathématiques

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  2015-2019).
Member of the scientific board of the university (2008-2016).
Member of the board of CYU - University of Cergy-Pontoise (2020-2023).
International Mathematics Research Notices (principal editor).
International Journal of Differential Equations (associate editor).
Potential Analysis (associate editor).
Tunisian Journal of Mathematics
(associate editor).
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 BooksIcon
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
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, Math Icon
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] Super critical energy scale invariant equations in critical spaces, SuperCrit.pdf,
6 pages, 2010.
Rewriting of a known result.
[6] [New] A short (informal) introduction to Bopp-Podolsky-Schrödinger-Proca
and Schrödinger-Poisson-Proca systems in the electro-magneto-static case,
BPSPHebeySurvey.pdf, 20 pages, 2020.

Transparents / Slides from various talks:
[1] Existence, stability and instability for Einstein-scalar field Lichnerowicz
equations, EinLich.pdf, Slides, Contains unpublished results, 46 pages, 2008/2009.
[2] Elliptic stability for stationary Schrödinger equations, Retro Projecteur
Part I, PartII, and PartIII.
Slides from a three parts course given in 2013.
[3] Companion tables for the above slides on elliptic stability, Tables, 2013.
[New] Updated version, March 2021, UpdatedVersion2021.
[4] 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.
[5] Klein-Gordon-Maxwell-Proca systems in closed manifolds, KGMPSlides, Slides
from a talk, 37 pages, 2014.
[6] Nonnegative solutions of stationary Kirchhoff systems, KirchhoffSyst, Slides
from a talk, 30 pages, 2015.
[7] Sationary Kirchhoff equations with powers, KPowersSlides, Slides
from a talk, 32 pages, 2017.
Klein-Gordon-Maxwell-Proca systems in the Riemannian setting, KGMPSlides2,
Slides from a talk, 39 pages, 2018.

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, 9991059, 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, 37033718, 2013.
[10] The Lichnerowicz equation in the closed case of the Einstein-Maxwell theory,
avec G.Veronelli,
Transactions of the American Mathematical Society
366, 11791193, 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, 
in Partial Differential Equations, 41, 913-924, 2016.

[16] Stationary Kirchhoff equations with powers,
Advances in the Calculus of Variations
, 11, 139-160, 2018.
[17] Klein-Gordon-Maxwell-Proca type systems in the electro-magneto-static case,
avec P.D.Thizy,
Journal of Partial Differential Equations
, 31, 119-158, 2018.
Klein-Gordon-Maxwell-Proca type systems in the electro-magneto-static case: the high  dimensional case, avec P.D.Thizy,
Calculus of Variations and Partial Differential Equations,
58, 116 (31 pages), 2019.
Electro-Magnetic-Static study of the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca Setting,
Discrete and Continuous Dynamical Systems - Series A, 39, 6683-6712, 2019.
[20] Strong convergence of the Bopp-Podolsky-Schrödinger-Proca system to the
Schrödinger-Poisson-Proca system in the electro-magneto-static case,
Calculus of Variations and Partial Differential Equations, à paraître.
[21] Schrödinger-Poisson-Proca systems in EMS regime,
Communications in Contemporary Mathematics
à paraître.

Comités éditoriaux:
International Journal of Differential Equations (associate editor),
International Mathematics Research Notices
(principal editor),
Potential Analysis (associate editor),
Tunisian Journal of Mathematics
(associate editor).

Quelques conférences:
Modern Trends in PDE's, Geometric Analysis and Mathematical Physics
(Sept. 2011, org. V.Georgescu, E.Hebey et A.Shirikyan, université de Cergy-Pontoise)
Recent trends in geometric and nonlinear analysis
(Août 2012, org. E.Hebey et F.Robert, Banff International Research Station, Canada)
Cocompact Imbeddings, Profile Decompositions, and their Applications to PDE
(Janvier 2012, membre du comité scientifique, Tata Institute of Fundamental Research, Bangalore, Inde)
Géométrie conforme et géométrie Kählérienne
(Sept. à Dec. 2012, Trimestre de l'Institut Henri-Poincaré, org. M.Gursky, E.Hebey, F.Pacard, J.Viaclovsky)
Three weeks Thematic Program on Nonlinear PDEs in Geometry and Physics
(Summer 2014, University of Notre-Dame, Indiana, org. M.Gursky, E.Hebey)
Asymptotics for Nonlinear Geometric PDEs
(Nov.2014, SNS Pisa, org. E.Hebey, G.Lebeau, F.Merle, F.Planchon, N.Visciglia)
Nonlinear Analysis in Rome
(June 2017, Rome, org. M. Gursky, E.Hebey, A.Malchiodi).
Conférence en l'honneur des 25 ans des laboratoires AGM et LPTM
(June 2017, Cergy-Pontoise, org. E.Hebey, F.Koukiou).

Calcul Différentiel Avancé: Chapitre 1 , Chapitre 2 , Chapitre 3 , Chapitre 4 ,
Chapitre 5 , Chapitre 6 , Chapitre 7 , Chapitre 8
Algèbre bilinéaire et intégration: La page du cours 2019-2020

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