{"title":"小临界指数的离散子群","authors":"Beibei Liu, Shi Wang","doi":"10.2140/gt.2023.27.2347","DOIUrl":null,"url":null,"abstract":"We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than 1.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"183 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Discrete subgroups of small critical exponent\",\"authors\":\"Beibei Liu, Shi Wang\",\"doi\":\"10.2140/gt.2023.27.2347\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than 1.\",\"PeriodicalId\":254292,\"journal\":{\"name\":\"Geometry & Topology\",\"volume\":\"183 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry & Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gt.2023.27.2347\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gt.2023.27.2347","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than 1.
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