Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-11-17 DOI:10.1112/blms.13189

Qiyu Chen, Jean-Marc Schlenker

{"title":"Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes","authors":"Qiyu Chen, Jean-Marc Schlenker","doi":"10.1112/blms.13189","DOIUrl":null,"url":null,"abstract":"Let <math>\n <semantics>\n <mi>S</mi>\n <annotation>$S$</annotation>\n </semantics></math> be a closed surface of genus at least 2, let <math>\n <semantics>\n <mi>h</mi>\n <annotation>$h$</annotation>\n </semantics></math> be a smooth metric of curvature <math>\n <semantics>\n <mrow>\n <mi>K</mi>\n <mo><</mo>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$K<-1$</annotation>\n </semantics></math> on <math>\n <semantics>\n <mi>S</mi>\n <annotation>$S$</annotation>\n </semantics></math>, and let <math>\n <semantics>\n <msub>\n <mi>h</mi>\n <mn>0</mn>\n </msub>\n <annotation>$h_0$</annotation>\n </semantics></math> be a hyperbolic metric on <math>\n <semantics>\n <mi>S</mi>\n <annotation>$S$</annotation>\n </semantics></math>. We show that there exists a unique quasifuchsian AdS spacetime with left metric isotopic to <math>\n <semantics>\n <msub>\n <mi>h</mi>\n <mn>0</mn>\n </msub>\n <annotation>$h_0$</annotation>\n </semantics></math>, containing a past-convex Cauchy surface with induced metric isotopic to <math>\n <semantics>\n <mi>h</mi>\n <annotation>$h$</annotation>\n </semantics></math>.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"164-180"},"PeriodicalIF":0.8000,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13189","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

Let $S$ be a closed surface of genus at least 2, let $h$ be a smooth metric of curvature $K < - 1$ on $S$ , and let $h_{0}$ be a hyperbolic metric on $S$ . We show that there exists a unique quasifuchsian AdS spacetime with left metric isotopic to $h_{0}$ , containing a past-convex Cauchy surface with induced metric isotopic to $h$ .