{"title":"Sublinearly Morse boundary of CAT(0) admissible groups","authors":"Hoang Thanh Nguyen, Yulan Qing","doi":"10.1515/jgth-2023-0145","DOIUrl":null,"url":null,"abstract":"We show that if 𝐺 is an admissible group acting geometrically on a <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>CAT</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mn>0</m:mn> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0145_ineq_0001.png\" /> <jats:tex-math>\\operatorname{CAT}(0)</jats:tex-math> </jats:alternatives> </jats:inline-formula> space 𝑋, then 𝐺 is a hierarchically hyperbolic space and its 𝜅-Morse boundary <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:msub> <m:mo lspace=\"0em\" rspace=\"0em\">∂</m:mo> <m:mi>κ</m:mi> </m:msub> <m:mi>G</m:mi> </m:mrow> <m:mo>,</m:mo> <m:mi>ν</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0145_ineq_0002.png\" /> <jats:tex-math>(\\partial_{\\kappa}G,\\nu)</jats:tex-math> </jats:alternatives> </jats:inline-formula> is a model for the Poisson boundary of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>G</m:mi> <m:mo>,</m:mo> <m:mi>μ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0145_ineq_0003.png\" /> <jats:tex-math>(G,\\mu)</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where 𝜈 is the hitting measure associated to the random walk driven by 𝜇.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2023-0145","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We show that if 𝐺 is an admissible group acting geometrically on a CAT(0)\operatorname{CAT}(0) space 𝑋, then 𝐺 is a hierarchically hyperbolic space and its 𝜅-Morse boundary (∂κG,ν)(\partial_{\kappa}G,\nu) is a model for the Poisson boundary of (G,μ)(G,\mu), where 𝜈 is the hitting measure associated to the random walk driven by 𝜇.
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