{"title":"The Dirichlet problem for the complex\n homogeneous Monge-Ampère equation","authors":"J. Ross, D. Nystrom","doi":"10.1090/PSPUM/099/01744","DOIUrl":null,"url":null,"abstract":"We survey the Dirichlet problem for the complex Homogeneous Monge-Amp\\`ere Equation, both in the case of domains in $\\mathbb C^n$ and the case of compact K\\\"ahler manifolds parametrized by a Riemann surface with boundary. We then give a self-contained account of previous work of the authors that connects this with the Hele-Shaw flow, and give several concrete examples illustrating various phenomena that solutions to this problem can display.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of Symposia in Pure\n Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/PSPUM/099/01744","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
We survey the Dirichlet problem for the complex Homogeneous Monge-Amp\`ere Equation, both in the case of domains in $\mathbb C^n$ and the case of compact K\"ahler manifolds parametrized by a Riemann surface with boundary. We then give a self-contained account of previous work of the authors that connects this with the Hele-Shaw flow, and give several concrete examples illustrating various phenomena that solutions to this problem can display.
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