{"title":"Liouville Theorem for harmonic maps from Riemannian manifold with compact boundary","authors":"Jun Sun, Xiaobao Zhu","doi":"10.2996/kmj46204","DOIUrl":null,"url":null,"abstract":"In this note we will provide a gradient estimate for harmonic maps from a complete noncompact Riemannian manifold with compact boundary (which we call\"Kasue manifold\") into a simply connected complete Riemannian manifold with non-positive sectional curvature. As a consequence, we can obtain a Liouville theorem. We will also show the nonexistence of positive solutions to some linear elliptic equation on Kasue manifold.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kodai Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2996/kmj46204","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this note we will provide a gradient estimate for harmonic maps from a complete noncompact Riemannian manifold with compact boundary (which we call"Kasue manifold") into a simply connected complete Riemannian manifold with non-positive sectional curvature. As a consequence, we can obtain a Liouville theorem. We will also show the nonexistence of positive solutions to some linear elliptic equation on Kasue manifold.
期刊介绍:
Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.