[Solutions faibles des équations de Monge–Ampère complexes 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.
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.
Accepté le :
Publié le :
Slimane Benelkourchi 1
@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}, }
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] 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
[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
[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
- Weak Solutions to Complex Hessian Type Equations in the Class
, Vietnam Journal of Mathematics, Volume 52 (2024) no. 1, p. 117 | DOI:10.1007/s10013-022-00562-7 - Continuous Solutions for Degenerate Complex Hessian Equation, Acta Mathematica Vietnamica, Volume 48 (2023) no. 2, p. 371 | DOI:10.1007/s40306-023-00498-1
- Envelope Approach to Degenerate Complex Monge–Ampère Equations on Compact Kähler Manifolds, Canadian Mathematical Bulletin, Volume 60 (2017) no. 4, p. 705 | DOI:10.4153/cmb-2017-048-7
Cité par 3 documents. Sources : Crossref
Commentaires - Politique