{"title":"Rotators-translators to mean curvature flow in \\(\\mathbb {H}^2\\times \\mathbb {R}\\)","authors":"R. F. de Lima, A. K. Ramos, J. P. dos Santos","doi":"10.1007/s00013-024-02076-9","DOIUrl":null,"url":null,"abstract":"<div><p>We establish the existence of one-parameter families of helicoidal surfaces of <span>\\(\\mathbb H^2\\times \\mathbb R\\)</span> which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"343 - 353"},"PeriodicalIF":0.5000,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-02076-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We establish the existence of one-parameter families of helicoidal surfaces of \(\mathbb H^2\times \mathbb R\) which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.
期刊介绍:
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.