[La méthode de continuité de Ricci pour lʼéquation de Monge–Ampère complexe, avec des applications aux métriques de Kähler–Einstein conique le long dʼarêtes]
Dans cette Note nous introduisons une nouvelle méthode de continuité et estimée a priori, pour lʼéquation de Monge–Ampère complexe dégénérée. Nous présentons également quelques applications de cette méthode à lʼexistence de métriques de Kähler–Einstein ayant une structure conique le long dʼarêtes, confirm des conjectures de Tian et de Donaldson.
In this Note we present a new continuity method and a priori estimate for the degenerate complex Monge–Ampère equation. We then describe some applications of this method to the existence of Kähler–Einstein edge metrics, as conjectured by Tian and Donaldson.
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@article{CRMATH_2012__350_13-14_693_0,
author = {Rafe Mazzeo and Yanir A. Rubinstein},
title = {The {Ricci} continuity method for the complex {Monge{\textendash}Amp\`ere} equation, with applications to {K\"ahler{\textendash}Einstein} edge metrics},
journal = {Comptes Rendus. Math\'ematique},
pages = {693--697},
publisher = {Elsevier},
volume = {350},
number = {13-14},
year = {2012},
doi = {10.1016/j.crma.2012.07.001},
language = {en},
}
TY - JOUR AU - Rafe Mazzeo AU - Yanir A. Rubinstein TI - The Ricci continuity method for the complex Monge–Ampère equation, with applications to Kähler–Einstein edge metrics JO - Comptes Rendus. Mathématique PY - 2012 SP - 693 EP - 697 VL - 350 IS - 13-14 PB - Elsevier DO - 10.1016/j.crma.2012.07.001 LA - en ID - CRMATH_2012__350_13-14_693_0 ER -
%0 Journal Article %A Rafe Mazzeo %A Yanir A. Rubinstein %T The Ricci continuity method for the complex Monge–Ampère equation, with applications to Kähler–Einstein edge metrics %J Comptes Rendus. Mathématique %D 2012 %P 693-697 %V 350 %N 13-14 %I Elsevier %R 10.1016/j.crma.2012.07.001 %G en %F CRMATH_2012__350_13-14_693_0
Rafe Mazzeo; Yanir A. Rubinstein. The Ricci continuity method for the complex Monge–Ampère equation, with applications to Kähler–Einstein edge metrics. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 693-697. doi : 10.1016/j.crma.2012.07.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.001/
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