{"title":"Criteria for univalency and quasiconformal extension for harmonic mappings","authors":"Zhenyong Hu, Jinhua Fan","doi":"10.2996/kmj44203","DOIUrl":null,"url":null,"abstract":"In this paper, we study the univalency and quasiconformal extension of sense-preserving harmonic mappings $f$ in the unit disk. For $f$, we introduce a quantity similar to Ahlfors's criteria and obtain a criterion of univalency and quasiconformal extension of $f$, which can be regarded as generalizations of the results obtained by Ahlfors [Sufficient conditions for quasiconformal extension, Ann. of Math. Stud. 79 (1974), 23-29], Hernandez and Martin [Quasiconformal extensions of harmonic mappings in the plane, Ann. Acad. Sci. Fenn. Math. 38 (2013), 617-630], and Chen and Que [Quasiconformal extension of harmonic mappings with a complex parameter, J. Aust. Math. Soc. 102 (2017), 307-315]. By Schwarzian derivatives of harmonic mappings, we also obtain a criterion for univalency and quasiconformal extension for harmonic Techmuller mappings.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kodai Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2996/kmj44203","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: 1
Abstract
In this paper, we study the univalency and quasiconformal extension of sense-preserving harmonic mappings $f$ in the unit disk. For $f$, we introduce a quantity similar to Ahlfors's criteria and obtain a criterion of univalency and quasiconformal extension of $f$, which can be regarded as generalizations of the results obtained by Ahlfors [Sufficient conditions for quasiconformal extension, Ann. of Math. Stud. 79 (1974), 23-29], Hernandez and Martin [Quasiconformal extensions of harmonic mappings in the plane, Ann. Acad. Sci. Fenn. Math. 38 (2013), 617-630], and Chen and Que [Quasiconformal extension of harmonic mappings with a complex parameter, J. Aust. Math. Soc. 102 (2017), 307-315]. By Schwarzian derivatives of harmonic mappings, we also obtain a criterion for univalency and quasiconformal extension for harmonic Techmuller mappings.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
