长度函数在teichm勒和反德西特几何

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2023-11-17 DOI:10.1017/fms.2023.100

Filippo Mazzoli, Gabriele Viaggi

{"title":"长度函数在teichm<e:1>勒和反德西特几何","authors":"Filippo Mazzoli, Gabriele Viaggi","doi":"10.1017/fms.2023.100","DOIUrl":null,"url":null,"abstract":"We establish a link between the behavior of length functions on Teichmüller space and the geometry of certain anti-de Sitter $3$ -manifolds. As an application, we give new purely anti-de Sitter proofs of results of Teichmüller theory such as (strict) convexity of length functions along shear paths and geometric bounds on their second variation along earthquakes. Along the way, we provide shear-bend coordinates for GHMC anti-de Sitter $3$ -manifolds.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Length functions in Teichmüller and anti-de Sitter geometry\",\"authors\":\"Filippo Mazzoli, Gabriele Viaggi\",\"doi\":\"10.1017/fms.2023.100\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish a link between the behavior of length functions on Teichmüller space and the geometry of certain anti-de Sitter $3$ -manifolds. As an application, we give new purely anti-de Sitter proofs of results of Teichmüller theory such as (strict) convexity of length functions along shear paths and geometric bounds on their second variation along earthquakes. Along the way, we provide shear-bend coordinates for GHMC anti-de Sitter $3$ -manifolds.\",\"PeriodicalId\":56000,\"journal\":{\"name\":\"Forum of Mathematics Sigma\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Forum of Mathematics Sigma\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/fms.2023.100\",\"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":"Forum of Mathematics Sigma","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/fms.2023.100","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们建立了长度函数在teichm ller空间上的行为与某些反de Sitter $3$ -流形几何之间的联系。作为应用，我们给出了新的纯反德西特证明，如长度函数沿剪切路径的(严格)凸性和它们沿地震的二次变化的几何边界。在此过程中，我们提供了GHMC反德西特$3$流形的剪切弯曲坐标。

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

Length functions in Teichmüller and anti-de Sitter geometry

We establish a link between the behavior of length functions on Teichmüller space and the geometry of certain anti-de Sitter

$3$

-manifolds. As an application, we give new purely anti-de Sitter proofs of results of Teichmüller theory such as (strict) convexity of length functions along shear paths and geometric bounds on their second variation along earthquakes. Along the way, we provide shear-bend coordinates for GHMC anti-de Sitter

$3$

-manifolds.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.