Comptes Rendus
no. 7-8
Complex analysis
Weak solutions to complex Monge–Ampère equations on compact Kähler manifolds
[Solutions faibles des équations de Monge–Ampère complexes sur des variétés de Kähler compactes]

Présenté par : Jean-Pierre Demailly

Slimane Benelkourchi1
1 Université de Montréal, Pavillon 3744, rue Jean-Brillant, Montréal QC H3C 3J7, Canada
Comptes Rendus. Mathématique, Volume 352 (2014) no. 7-8, pp. 589-592.

Nous montrons un théorème général d'existence et d'unicité de solution d'une équation de type Monge–Ampère complexe sur des variétés de Kähler compactes.

We show a general existence theorem of solutions to the complex Monge–Ampère type equation on compact Kähler manifolds.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.06.003
Slimane Benelkourchi 1

1 Université de Montréal, Pavillon 3744, rue Jean-Brillant, Montréal QC H3C 3J7, Canada 
@article{CRMATH_2014__352_7-8_589_0,
     author = {Slimane Benelkourchi},
     title = {Weak solutions to complex {Monge{\textendash}Amp\`ere} equations on compact {K\"ahler} manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {589--592},
     publisher = {Elsevier},
     volume = {352},
     number = {7-8},
     year = {2014},
     doi = {10.1016/j.crma.2014.06.003},
     language = {en},
}
TY  - JOUR
AU  - Slimane Benelkourchi
TI  - Weak solutions to complex Monge–Ampère equations on compact Kähler manifolds
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 589
EP  - 592
VL  - 352
IS  - 7-8
PB  - Elsevier
DO  - 10.1016/j.crma.2014.06.003
LA  - en
ID  - CRMATH_2014__352_7-8_589_0
ER  - 
%0 Journal Article
%A Slimane Benelkourchi
%T Weak solutions to complex Monge–Ampère equations on compact Kähler manifolds
%J Comptes Rendus. Mathématique
%D 2014
%P 589-592
%V 352
%N 7-8
%I Elsevier
%R 10.1016/j.crma.2014.06.003
%G en
%F CRMATH_2014__352_7-8_589_0
Slimane Benelkourchi. Weak solutions to complex Monge–Ampère equations on compact Kähler manifolds. Comptes Rendus. Mathématique, Volume 352 (2014) no. 7-8, pp. 589-592. doi : 10.1016/j.crma.2014.06.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.06.003/

[1] T. Aubin Équations du type Monge–Ampère sur les variétés kählériennes compactes, C. R. Acad. Sci. Paris, Volume 283 (1976), pp. 119-121

[2] T. Aubin Équations du type Monge–Ampère sur les variétës kählériennes compactes, Bull. Sci. Math., Volume 102 (1978), pp. 63-95

[3] E. Bedford; B.A. Taylor A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982) no. 1–2, pp. 1-40

[4] E. Bedford; B.A. Taylor Fine topology, Šilov boundary, and (ddc)n, J. Funct. Anal., Volume 72 (1987) no. 2, pp. 225-251

[5] S. Benelkourchi; V. Guedj; A. Zeriahi A priori estimates for weak solutions of complex Monge–Ampère equations, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5), Volume VII (2008), pp. 1-16

[6] R.J. Berman; S. Boucksom; V. Guedj; A. Zeriahi A variational approach to complex Monge–Ampère equations, Publ. Math. Inst. Hautes Études Sci., Volume 117 (2013), pp. 179-245

[7] S. Boucksom; P. Eyssidieux; V. Guedj; A. Zeriahi Monge–Ampère equations in big cohomology classes, Acta Math., Volume 205 (2010) no. 2, pp. 199-262

[8] U. Cegrell; S. Kołodziej The equation of complex Monge–Ampère type and stability of solutions, Math. Ann., Volume 334 (2006) no. 4, pp. 713-729

[9] S. Dinew Uniqueness in E(X,ω), J. Funct. Anal., Volume 256 (2009) no. 7, pp. 2113-2122

[10] R.E. Edwards Functional Analysis: Theory and Applications, Holt-Rinehart and Winston, 1965

[11] V. Guedj; A. Zeriahi Intrinsic capacities on compact Kahler manifolds, J. Geom. Anal., Volume 15 (2005) no. 4, pp. 607-639

[12] V. Guedj; A. Zeriahi The weighted Monge–Ampère energy of quasiplurisubharmonic functions, J. Funct. Anal., Volume 250 (2007) no. 2, pp. 442-482

[13] Slawomir Kołodziej Weak solutions of equations of complex Monge–Ampère type, Ann. Pol. Math., Volume 73 (2000) no. 1, pp. 59-67

[14] Hoang Chinh Lu Solutions to degenerate complex Hessian equations, J. Math. Pures Appl., Volume 100 (2013), pp. 785-805

[15] S. Kołodziej The complex Monge–Ampère equation and pluripotential theory, Mem. Amer. Math. Soc., Volume 178 (2005) no. 840 (x+64 pp.)

[16] S.T. Yau On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampère equation. I, Commun. Pure Appl. Math., Volume 31 (1978) no. 3, pp. 339-411

Cité par Sources :

Commentaires - Politique