Weak solutions to complex Monge–Ampère equations on compact Kähler manifolds

Slimane Benelkourchi

doi:10.1016/j.crma.2014.06.003

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 Benelkourchi ¹

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.

Résumé
Abstract

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 : 2014-01-30
Accepté le : 2014-06-17
Publié le : 2014-07-01

DOI : 10.1016/j.crma.2014.06.003

Affiliations des auteurs :

Slimane Benelkourchi ¹

¹ Université de Montréal, Pavillon 3744, rue Jean-Brillant, Montréal QC H3C 3J7, Canada

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     title = {Weak solutions to complex {Monge{\textendash}Amp\`ere} equations on compact {K\"ahler} manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {589--592},
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     doi = {10.1016/j.crma.2014.06.003},
     language = {en},
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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/

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Hichame Amal; Saïd Asserda; Ayoub El-Gasmi Weak solutions to complex Hessian type equations in the class $E_{ϕ} (X, ω, m)$ , Vietnam Journal of Mathematics, Volume 52 (2024) no. 1, pp. 117-128 | DOI:10.1007/s10013-022-00562-7 | Zbl:1531.32042
Hichame Amal; Saïd Asserda; Manar Bouhssina Continuous solutions for degenerate complex Hessian equation, Acta Mathematica Vietnamica, Volume 48 (2023) no. 2, pp. 371-386 | DOI:10.1007/s40306-023-00498-1 | Zbl:1522.32089
Slimane Benelkourchi 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, zbMATH

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