线性Weingarten型的l_3中的平移孤子

IF 0.9 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI:10.1007/s10114-025-3330-3

Yu Fu, Rafael López, Yanru Luo, Dan Yang

{"title":"线性Weingarten型的l_3中的平移孤子","authors":"Yu Fu, Rafael López, Yanru Luo, Dan Yang","doi":"10.1007/s10114-025-3330-3","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider λ-translating solitons in ℝ<sup>3</sup>. These surfaces are critical points of the weighted area when the density is a coordinate function. If λ = 0, these surfaces evolve by translations along the mean curvature flow. We give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their curvatures. These surfaces are planes, circular cylinders, grim reapers and certain types of cylindrical surfaces. We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1617 - 1634"},"PeriodicalIF":0.9000,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Translating Solitons in ℝ3 of Linear Weingarten Type\",\"authors\":\"Yu Fu, Rafael López, Yanru Luo, Dan Yang\",\"doi\":\"10.1007/s10114-025-3330-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we consider λ-translating solitons in ℝ<sup>3</sup>. These surfaces are critical points of the weighted area when the density is a coordinate function. If λ = 0, these surfaces evolve by translations along the mean curvature flow. We give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their curvatures. These surfaces are planes, circular cylinders, grim reapers and certain types of cylindrical surfaces. We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":\"41 6\",\"pages\":\"1617 - 1634\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-025-3330-3\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-025-3330-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文考虑了在1 - 3中的λ平移孤子。当密度是一个坐标函数时，这些曲面是加权区域的关键点。如果λ = 0，这些曲面沿着平均曲率流的平移而演化。我们给出了λ平移孤子的完整分类，这些孤子的曲率之间满足线性Weingarten关系。这些表面是平面、圆柱、死神和某些类型的圆柱形表面。我们还证明了平面和圆柱是唯一具有二阶基本形式的常数平方范数的λ平移孤子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Translating Solitons in ℝ3 of Linear Weingarten Type

In this paper, we consider λ-translating solitons in ℝ³. These surfaces are critical points of the weighted area when the density is a coordinate function. If λ = 0, these surfaces evolve by translations along the mean curvature flow. We give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their curvatures. These surfaces are planes, circular cylinders, grim reapers and certain types of cylindrical surfaces. We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.