{"title":"给定Bartnik边界数据的静态真空扩展的存在性","authors":"Z. An, Lan-Hsuan Huang","doi":"10.4310/cjm.2022.v10.n1.a1","DOIUrl":null,"url":null,"abstract":"We prove the existence and local uniqueness of asymptotically flat, static vacuum metrics with arbitrarily prescribed Bartnik boundary data that are close to the induced boundary data on any star-shaped hypersurface or a general family of perturbed hypersurfaces in the Euclidean space. It confirms the existence part of the Bartnik static extension conjecture for large classes of boundary data, and the static vacuum metric obtained is geometrically unique in a neighborhood of the Euclidean metric.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Existence of static vacuum extensions with prescribed Bartnik boundary data\",\"authors\":\"Z. An, Lan-Hsuan Huang\",\"doi\":\"10.4310/cjm.2022.v10.n1.a1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the existence and local uniqueness of asymptotically flat, static vacuum metrics with arbitrarily prescribed Bartnik boundary data that are close to the induced boundary data on any star-shaped hypersurface or a general family of perturbed hypersurfaces in the Euclidean space. It confirms the existence part of the Bartnik static extension conjecture for large classes of boundary data, and the static vacuum metric obtained is geometrically unique in a neighborhood of the Euclidean metric.\",\"PeriodicalId\":48573,\"journal\":{\"name\":\"Cambridge Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cambridge Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cjm.2022.v10.n1.a1\",\"RegionNum\":2,\"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":"Cambridge Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cjm.2022.v10.n1.a1","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence of static vacuum extensions with prescribed Bartnik boundary data
We prove the existence and local uniqueness of asymptotically flat, static vacuum metrics with arbitrarily prescribed Bartnik boundary data that are close to the induced boundary data on any star-shaped hypersurface or a general family of perturbed hypersurfaces in the Euclidean space. It confirms the existence part of the Bartnik static extension conjecture for large classes of boundary data, and the static vacuum metric obtained is geometrically unique in a neighborhood of the Euclidean metric.