Voir la notice de l'article provenant de la source Numdam
We show a general existence theorem of solutions to the complex Monge–Ampère type equation on compact Kähler manifolds.
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.
Benelkourchi, Slimane 1
@article{CRMATH_2014__352_7-8_589_0, author = {Benelkourchi, Slimane}, 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}, url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2014.06.003/} }
TY - JOUR AU - Benelkourchi, Slimane 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 UR - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2014.06.003/ DO - 10.1016/j.crma.2014.06.003 LA - en ID - CRMATH_2014__352_7-8_589_0 ER -
%0 Journal Article %A Benelkourchi, Slimane %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 %U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2014.06.003/ %R 10.1016/j.crma.2014.06.003 %G en %F CRMATH_2014__352_7-8_589_0
Benelkourchi, Slimane. Weak solutions to complex Monge–Ampère equations on compact Kähler manifolds. Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 589-592. doi : 10.1016/j.crma.2014.06.003. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2014.06.003/
[1] Équations du type Monge–Ampère sur les variétés kählériennes compactes, C. R. Acad. Sci. Paris, Volume 283 (1976), pp. 119-121
[2] Équations du type Monge–Ampère sur les variétës kählériennes compactes, Bull. Sci. Math., Volume 102 (1978), pp. 63-95
[3] A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982) no. 1–2, pp. 1-40
[4] Fine topology, Šilov boundary, and , J. Funct. Anal., Volume 72 (1987) no. 2, pp. 225-251
[5] 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] A variational approach to complex Monge–Ampère equations, Publ. Math. Inst. Hautes Études Sci., Volume 117 (2013), pp. 179-245
[7] Monge–Ampère equations in big cohomology classes, Acta Math., Volume 205 (2010) no. 2, pp. 199-262
[8] The equation of complex Monge–Ampère type and stability of solutions, Math. Ann., Volume 334 (2006) no. 4, pp. 713-729
[9] Uniqueness in , J. Funct. Anal., Volume 256 (2009) no. 7, pp. 2113-2122
[10] Functional Analysis: Theory and Applications, Holt-Rinehart and Winston, 1965
[11] Intrinsic capacities on compact Kahler manifolds, J. Geom. Anal., Volume 15 (2005) no. 4, pp. 607-639
[12] The weighted Monge–Ampère energy of quasiplurisubharmonic functions, J. Funct. Anal., Volume 250 (2007) no. 2, pp. 442-482
[13] Weak solutions of equations of complex Monge–Ampère type, Ann. Pol. Math., Volume 73 (2000) no. 1, pp. 59-67
[14] Solutions to degenerate complex Hessian equations, J. Math. Pures Appl., Volume 100 (2013), pp. 785-805
[15] The complex Monge–Ampère equation and pluripotential theory, Mem. Amer. Math. Soc., Volume 178 (2005) no. 840 (x+64 pp.)
[16] 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 :