常曲率时空中Moncrief线的渐近性质

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-25 DOI:10.1112/blms.70032

Mehdi Belraouti, Abderrahim Mesbah, Lamine Messaci

{"title":"常曲率时空中Moncrief线的渐近性质","authors":"Mehdi Belraouti, Abderrahim Mesbah, Lamine Messaci","doi":"10.1112/blms.70032","DOIUrl":null,"url":null,"abstract":"We study the asymptotic behavior of Moncrief lines on <math>\n <semantics>\n <mrow>\n <mn>2</mn>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$2+1$</annotation>\n </semantics></math> maximal globally hyperbolic spatially compact space-time <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> of nonnegative constant curvature. We show that when the unique geodesic lamination associated with <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> is either maximal uniquely ergodic or simplicial, the Moncrief line converges, as time goes to zero, to a unique point in the Thurston boundary of the Teichmüller space.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1347-1359"},"PeriodicalIF":0.8000,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70032","citationCount":"0","resultStr":"{\"title\":\"Asymptotic behavior of Moncrief Lines in constant curvature space-times\",\"authors\":\"Mehdi Belraouti, Abderrahim Mesbah, Lamine Messaci\",\"doi\":\"10.1112/blms.70032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the asymptotic behavior of Moncrief lines on <math>\\n <semantics>\\n <mrow>\\n <mn>2</mn>\\n <mo>+</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$2+1$</annotation>\\n </semantics></math> maximal globally hyperbolic spatially compact space-time <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math> of nonnegative constant curvature. We show that when the unique geodesic lamination associated with <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math> is either maximal uniquely ergodic or simplicial, the Moncrief line converges, as time goes to zero, to a unique point in the Thurston boundary of the Teichmüller space.\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"57 5\",\"pages\":\"1347-1359\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70032\",\"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.70032\",\"RegionNum\":3,\"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":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.70032","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

摘要

研究了非负常曲率的2+1$ 2+1$极大整体双曲空间紧时空M$ M$上Moncrief线的渐近行为。我们证明了当与M$ M$相关联的唯一测地线层合是极大唯一遍历的或简单的，当时间趋近于0时，Moncrief线收敛于teichm空间的Thurston边界上的一个唯一点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Asymptotic behavior of Moncrief Lines in constant curvature space-times

We study the asymptotic behavior of Moncrief lines on $2 + 1$ maximal globally hyperbolic spatially compact space-time $M$ of nonnegative constant curvature. We show that when the unique geodesic lamination associated with $M$ is either maximal uniquely ergodic or simplicial, the Moncrief line converges, as time goes to zero, to a unique point in the Thurston boundary of the Teichmüller space.