Emmanuel Hebey
Professeur des universités

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

Université de Cergy-Pontoise
Département de Mathématiques
2 avenue Adolphe Chauvin
95302 Cergy-Pontoise cedex

hebey(at)u-cergy.fr , or

Curriculum Vitae

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.
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.
ull 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).
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 DjadliOlivier Druet, Antoinette
Jourdain, Benoit Pausader, Bruno Premoselli, Frédéric RobertNicolas 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
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, 291 pages, European
Mathematical Society, To appear.

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(Unpublished texts with free access)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] Klein-Gordon-Maxwell-Proca systems in closed manifolds, KGMPSlides, Slides
from a talk, 37 pages, 2014.

Quelques articles récents:
(Some recent research papers)
[1] A variational analysis of Einstein-scalar field Lichnerowicz equations
on compact Riemannian manifolds, avec F.Pacard et D.Pollack,
Communications in Mathematical
Physics, 278, 117
132, 2008.
[2] Stability and instability for Einstein-scalar field Lichnerowicz
equations on compact Riemannian manifolds, avec O.Druet,
Mathematische Zeitschrift
, 263, 33
67, 2009.
[3] Stability for strongly coupled critical elliptic systems in a fully
inhomogeneous medium, avec O. Druet,
Analysis & PDE
, 2, 305–359, 2009.
[4] 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.
[5] The Lin-Ni's conjecture for vector valued Schrödinger equations in
the closed case,
Communications in Pure and Applied Analysis
, 9, 955–962, 2010.
[6] 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.
[7] Asymptotic analysis for fourth order Paneitz equations with critical
growth, avec F.Robert,
Advances in the Calculus of Variations, 3, 229
276, 2011.
[8] 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.
[9] Solitary waves in critical Abelian gauge theories,
Discrete and Continuous Dynamical Systems - Series A, 32, 1747
1761, 2012.
[10] Resonant states for the static Klein-Gordon-Maxwell-Proca system, avec J.Wei,
Mathematical Research Letters, 19, 4, 953
967, 2012.
[11] Schrödinger-Poisson systems in the 3-sphere, avec J.Wei, 33 pages,
Calculus of Variations and Partial Differential Equations, 47, 25-54, 2013.

[12] Stability of elliptic PDEs with respect to perturbations of the domain, avec O.Druet
et P.Laurain,
Journal of Differential Equations,
10, 37033718, 2013.
[13] The Lichnerowicz equation in the closed case of the Einstein-Maxwell theory,
avec G.Veronelli,
Transactions of the American Mathematical Society,
366, 11791193, 2014.
[14] 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)
, 29 pages, à paraître.

Quelques conférences récentes
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)

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
Le serveur mathworld


Mise à jour: Mars 2014