{"title":"具有强伪凸边界的斯泰因空间上的伯格曼-爱因斯坦度量","authors":"Huang,Xiaojun, Li,Xiaoshan","doi":"10.4310/cag.2023.v31.n7.a3","DOIUrl":null,"url":null,"abstract":"Let $\\Omega $ be a Stein space with a compact smooth strongly pseudoconvex boundary. We prove that the boundary is spherical if its Bergman metric over $\\text{Reg}(\\Omega )$ is Kähler-Einstein.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bergman-Einstein metric on a Stein space with a strongly pseudoconvex boundary\",\"authors\":\"Huang,Xiaojun, Li,Xiaoshan\",\"doi\":\"10.4310/cag.2023.v31.n7.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $\\\\Omega $ be a Stein space with a compact smooth strongly pseudoconvex boundary. We prove that the boundary is spherical if its Bergman metric over $\\\\text{Reg}(\\\\Omega )$ is Kähler-Einstein.\",\"PeriodicalId\":50662,\"journal\":{\"name\":\"Communications in Analysis and Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cag.2023.v31.n7.a3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cag.2023.v31.n7.a3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Bergman-Einstein metric on a Stein space with a strongly pseudoconvex boundary
Let $\Omega $ be a Stein space with a compact smooth strongly pseudoconvex boundary. We prove that the boundary is spherical if its Bergman metric over $\text{Reg}(\Omega )$ is Kähler-Einstein.
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