关于有边界流形上Obata方程的一个注记

IF 0.8 4区数学

数学研究 Pub Date : 2022-06-01 DOI:10.4208/jms.v55n3.22.02

Mijia Lai null, Hui Zhou

{"title":"关于有边界流形上Obata方程的一个注记","authors":"Mijia Lai null, Hui Zhou","doi":"10.4208/jms.v55n3.22.02","DOIUrl":null,"url":null,"abstract":". We analyze complete manifolds with boundary which admit solutions to Obata type equations ∇ 2 f − f g = 0 and ∇ 2 f = g under various boundary conditions. Given the existence of interior critical points, such manifolds are domains in the hyperbolic space and the Euclidean space respectively.","PeriodicalId":43526,"journal":{"name":"数学研究","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Note on Obata Equations on Manifolds with Boundary\",\"authors\":\"Mijia Lai null, Hui Zhou\",\"doi\":\"10.4208/jms.v55n3.22.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We analyze complete manifolds with boundary which admit solutions to Obata type equations ∇ 2 f − f g = 0 and ∇ 2 f = g under various boundary conditions. Given the existence of interior critical points, such manifolds are domains in the hyperbolic space and the Euclidean space respectively.\",\"PeriodicalId\":43526,\"journal\":{\"name\":\"数学研究\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学研究\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/jms.v55n3.22.02\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jms.v55n3.22.02","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

．我们分析了在不同边界条件下Obata型方程∇2f−f g = 0和∇2f = g有边界的完全流形。在给定内临界点存在的情况下，这种流形分别是双曲空间和欧几里德空间中的域。

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

A Note on Obata Equations on Manifolds with Boundary

. We analyze complete manifolds with boundary which admit solutions to Obata type equations ∇ 2 f − f g = 0 and ∇ 2 f = g under various boundary conditions. Given the existence of interior critical points, such manifolds are domains in the hyperbolic space and the Euclidean space respectively.

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

数学研究 MATHEMATICS-

自引率

0.00%

发文量

1109

期刊介绍： Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.