完全流形上正标量曲率的几何

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik Pub Date : 2022-01-29 DOI:10.1515/crelle-2022-0049

Bo Zhu

{"title":"完全流形上正标量曲率的几何","authors":"Bo Zhu","doi":"10.1515/crelle-2022-0049","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. On three-dimensional manifold, we prove a minimal volume growth, an estimate of integral of scalar curvature and width. On higher-dimensional manifold, we obtain a volume growth with a stronger condition.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2022-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Geometry of positive scalar curvature on complete manifold\",\"authors\":\"Bo Zhu\",\"doi\":\"10.1515/crelle-2022-0049\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. On three-dimensional manifold, we prove a minimal volume growth, an estimate of integral of scalar curvature and width. On higher-dimensional manifold, we obtain a volume growth with a stronger condition.\",\"PeriodicalId\":54896,\"journal\":{\"name\":\"Journal fur die Reine und Angewandte Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-01-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal fur die Reine und Angewandte Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/crelle-2022-0049\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal fur die Reine und Angewandte Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/crelle-2022-0049","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 10

摘要

摘要本文研究了具有非负Ricci曲率的完全非紧流形上几何与正标量曲率的相互作用。在三维流形上，我们证明了一个最小体积增长，一个标量曲率和宽度积分的估计。在高维流形上，我们得到了一个更强条件下的体积增长。

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

Geometry of positive scalar curvature on complete manifold

Abstract In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. On three-dimensional manifold, we prove a minimal volume growth, an estimate of integral of scalar curvature and width. On higher-dimensional manifold, we obtain a volume growth with a stronger condition.

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

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.