Anosov群保形测度的唯一性与局部混合

IF 0.8 3区数学 Q2 MATHEMATICS

Michigan Mathematical Journal Pub Date : 2021-11-24 DOI:10.1307/mmj/20217222

Sam O. Edwards, Minju M. Lee, H. Oh

{"title":"Anosov群保形测度的唯一性与局部混合","authors":"Sam O. Edwards, Minju M. Lee, H. Oh","doi":"10.1307/mmj/20217222","DOIUrl":null,"url":null,"abstract":"Abstract. In the late seventies, Sullivan showed that for a convex cocompact subgroup Γ of SO(n, 1) with critical exponent δ > 0, any Γ-conformal measure on ∂H of dimension δ is necessarily supported on the limit set Λ and that the conformal measure of dimension δ exists uniquely. We prove an analogue of this theorem for any Zariski dense Anosov subgroup Γ of a connected semisimple real algebraic group G of rank at most 3. We also obtain the local mixing for generalized BMS measures on Γ\\G including Haar measures.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"183 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Uniqueness of Conformal Measures and Local Mixing for Anosov Groups\",\"authors\":\"Sam O. Edwards, Minju M. Lee, H. Oh\",\"doi\":\"10.1307/mmj/20217222\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. In the late seventies, Sullivan showed that for a convex cocompact subgroup Γ of SO(n, 1) with critical exponent δ > 0, any Γ-conformal measure on ∂H of dimension δ is necessarily supported on the limit set Λ and that the conformal measure of dimension δ exists uniquely. We prove an analogue of this theorem for any Zariski dense Anosov subgroup Γ of a connected semisimple real algebraic group G of rank at most 3. We also obtain the local mixing for generalized BMS measures on Γ\\\\G including Haar measures.\",\"PeriodicalId\":49820,\"journal\":{\"name\":\"Michigan Mathematical Journal\",\"volume\":\"183 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Michigan Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1307/mmj/20217222\",\"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":"Michigan Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1307/mmj/20217222","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: 12

摘要

摘要在七十年代末，Sullivan证明了对于临界指数δ > 0的SO(n, 1)的凸紧子群Γ，在极限集Λ上，∂H上的任何一个δ维的Γ-conformal测度都必然被支持，并且δ维的保形测度唯一存在。对于秩不超过3的连通半单实数代数群G的任意Zariski密集Anosov子群Γ，证明了该定理的一个类似。我们还得到了Γ\G上包含Haar测度的广义BMS测度的局部混合。

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

Uniqueness of Conformal Measures and Local Mixing for Anosov Groups

Abstract. In the late seventies, Sullivan showed that for a convex cocompact subgroup Γ of SO(n, 1) with critical exponent δ > 0, any Γ-conformal measure on ∂H of dimension δ is necessarily supported on the limit set Λ and that the conformal measure of dimension δ exists uniquely. We prove an analogue of this theorem for any Zariski dense Anosov subgroup Γ of a connected semisimple real algebraic group G of rank at most 3. We also obtain the local mixing for generalized BMS measures on Γ\G including Haar measures.

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

Michigan Mathematical Journal 数学-数学

CiteScore

1.20

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Michigan Mathematical Journal is available electronically through the Project Euclid web site. The electronic version is available free to all paid subscribers. The Journal must receive from institutional subscribers a list of Internet Protocol Addresses in order for members of their institutions to have access to the online version of the Journal.