{"title":"Willmore surfaces in spheres: the DPW approach via the conformal Gauss map","authors":"Josef F. Dorfmeister, Peng Wang","doi":"10.1007/s12188-019-00204-9","DOIUrl":null,"url":null,"abstract":"<div><p>The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in <span>\\({\\mathbb {R}}^{n+2}\\)</span>, isotropic surfaces in <span>\\(S^4\\)</span> and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in <span>\\(S^6\\)</span> without dual surfaces is also presented.\n</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00204-9","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s12188-019-00204-9","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: 6
Abstract
The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in \({\mathbb {R}}^{n+2}\), isotropic surfaces in \(S^4\) and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in \(S^6\) without dual surfaces is also presented.
期刊介绍：
The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.
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