负曲面上封闭测地线的比较定理

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-02-22 DOI:10.4171/ggd/671

S. Cantrell, M. Pollicott

{"title":"负曲面上封闭测地线的比较定理","authors":"S. Cantrell, M. Pollicott","doi":"10.4171/ggd/671","DOIUrl":null,"url":null,"abstract":"In this note we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In particular, we provide an averaged comparison of these two important quantities and obtain precise statistical results, including a central limit theorem and a local limit theorem. Further, as a corollary we also improve an asymptotic formula of R. Sharp and the second author. Finally, we relate our results to recent work of Gekhtman, Taylor and Tiozzo.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2020-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Comparison theorems for closed geodesics on negatively curved surfaces\",\"authors\":\"S. Cantrell, M. Pollicott\",\"doi\":\"10.4171/ggd/671\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In particular, we provide an averaged comparison of these two important quantities and obtain precise statistical results, including a central limit theorem and a local limit theorem. Further, as a corollary we also improve an asymptotic formula of R. Sharp and the second author. Finally, we relate our results to recent work of Gekhtman, Taylor and Tiozzo.\",\"PeriodicalId\":55084,\"journal\":{\"name\":\"Groups Geometry and Dynamics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Geometry and Dynamics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/ggd/671\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Geometry and Dynamics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/ggd/671","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

在本文中，我们给出了新的渐近估计，比较了具有（可变）负截面曲率的曲面上闭合测地线的字长和测地线长度。特别地，我们提供了这两个重要量的平均比较，并获得了精确的统计结果，包括中心极限定理和局部极限定理。此外，作为推论，我们还改进了R.Sharp和第二作者的一个渐近公式。最后，我们将我们的结果与Gekhtman、Taylor和Tiozzo最近的工作联系起来。

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

Comparison theorems for closed geodesics on negatively curved surfaces

In this note we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In particular, we provide an averaged comparison of these two important quantities and obtain precise statistical results, including a central limit theorem and a local limit theorem. Further, as a corollary we also improve an asymptotic formula of R. Sharp and the second author. Finally, we relate our results to recent work of Gekhtman, Taylor and Tiozzo.

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

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.