{"title":"革命曲面上曲线缩短流的旋转孤子","authors":"B. Leandro, R. Novais, H. Reis","doi":"10.1007/s00025-024-02219-y","DOIUrl":null,"url":null,"abstract":"<p>We present a characterization for the rotational soliton for the curve shortening flow (CSF) on the revolution surfaces of <span>\\(\\mathbb {R}^3\\)</span>. Furthermore, we describe the behavior of such curves by showing that the two ends of each open curve are asymptotic to a parallel geodesic.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rotational Solitons for the Curve Shortening Flow on Revolution Surfaces\",\"authors\":\"B. Leandro, R. Novais, H. Reis\",\"doi\":\"10.1007/s00025-024-02219-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We present a characterization for the rotational soliton for the curve shortening flow (CSF) on the revolution surfaces of <span>\\\\(\\\\mathbb {R}^3\\\\)</span>. Furthermore, we describe the behavior of such curves by showing that the two ends of each open curve are asymptotic to a parallel geodesic.</p>\",\"PeriodicalId\":54490,\"journal\":{\"name\":\"Results in Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Results in Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00025-024-02219-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00025-024-02219-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Rotational Solitons for the Curve Shortening Flow on Revolution Surfaces
We present a characterization for the rotational soliton for the curve shortening flow (CSF) on the revolution surfaces of \(\mathbb {R}^3\). Furthermore, we describe the behavior of such curves by showing that the two ends of each open curve are asymptotic to a parallel geodesic.
期刊介绍：
Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.
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