{"title":"复杂蒙日-安培方程的渐近性和收敛性","authors":"Qing Han, Xumin Jiang","doi":"10.1007/s40818-024-00171-2","DOIUrl":null,"url":null,"abstract":"<div><p>We study the asymptotics of complete Kähler-Einstein metrics on strictly pseudoconvex domains in <span>\\(\\mathbb {C}^n\\)</span> and derive a convergence theorem for solutions to the corresponding Monge-Ampère equation. If only a portion of the boundary is analytic, the solutions satisfy Gevrey type estimates for tangential derivatives. A counterexample for the model linearized equation suggests that there is no local convergence theorem for the complex Monge-Ampère equation.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotics and Convergence for the Complex Monge-Ampère Equation\",\"authors\":\"Qing Han, Xumin Jiang\",\"doi\":\"10.1007/s40818-024-00171-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the asymptotics of complete Kähler-Einstein metrics on strictly pseudoconvex domains in <span>\\\\(\\\\mathbb {C}^n\\\\)</span> and derive a convergence theorem for solutions to the corresponding Monge-Ampère equation. If only a portion of the boundary is analytic, the solutions satisfy Gevrey type estimates for tangential derivatives. A counterexample for the model linearized equation suggests that there is no local convergence theorem for the complex Monge-Ampère equation.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-024-00171-2\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-024-00171-2","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Asymptotics and Convergence for the Complex Monge-Ampère Equation
We study the asymptotics of complete Kähler-Einstein metrics on strictly pseudoconvex domains in \(\mathbb {C}^n\) and derive a convergence theorem for solutions to the corresponding Monge-Ampère equation. If only a portion of the boundary is analytic, the solutions satisfy Gevrey type estimates for tangential derivatives. A counterexample for the model linearized equation suggests that there is no local convergence theorem for the complex Monge-Ampère equation.
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