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.
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.
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@article{CRMATH_2012__350_13-14_693_0, author = {Mazzeo, Rafe and Rubinstein, Yanir A.}, 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}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.07.001/} }
TY - JOUR AU - Mazzeo, Rafe AU - Rubinstein, Yanir A. 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 UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.07.001/ DO - 10.1016/j.crma.2012.07.001 LA - en ID - CRMATH_2012__350_13-14_693_0 ER -
%0 Journal Article %A Mazzeo, Rafe %A Rubinstein, Yanir A. %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 %U http://archive.numdam.org/articles/10.1016/j.crma.2012.07.001/ %R 10.1016/j.crma.2012.07.001 %G en %F CRMATH_2012__350_13-14_693_0
Mazzeo, Rafe; Rubinstein, Yanir A. 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. http://archive.numdam.org/articles/10.1016/j.crma.2012.07.001/
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