{"title":"论非正曲率有限体积非紧凑流形的末端","authors":"Ran Ji, Yunhui Wu","doi":"10.1007/s00222-024-01266-0","DOIUrl":null,"url":null,"abstract":"<p>In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold <span>\\(M\\)</span> of finite volume with sectional curvature <span>\\(-1 \\leq K \\leq 0\\)</span>, if the universal cover of <span>\\(M\\)</span> is a visibility manifold, then the fundamental group of each end of <span>\\(M\\)</span> is almost nilpotent.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On ends of finite-volume noncompact manifolds of nonpositive curvature\",\"authors\":\"Ran Ji, Yunhui Wu\",\"doi\":\"10.1007/s00222-024-01266-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold <span>\\\\(M\\\\)</span> of finite volume with sectional curvature <span>\\\\(-1 \\\\leq K \\\\leq 0\\\\)</span>, if the universal cover of <span>\\\\(M\\\\)</span> is a visibility manifold, then the fundamental group of each end of <span>\\\\(M\\\\)</span> is almost nilpotent.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00222-024-01266-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00222-024-01266-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中，我们证实了一个民间猜想，即对于一个具有截面曲率（-1 \leq K \leq 0\）的有限体积的完整非紧密流形（M\），如果（M\）的普盖是一个可见流形，那么（M\）的每个端部的基群几乎都是零potent。
On ends of finite-volume noncompact manifolds of nonpositive curvature
In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold \(M\) of finite volume with sectional curvature \(-1 \leq K \leq 0\), if the universal cover of \(M\) is a visibility manifold, then the fundamental group of each end of \(M\) is almost nilpotent.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
