{"title":"（\\mathbb｛R｝^4\\）中平均曲率流平移孤立子的SO（2）对称性","authors":"Jingze Zhu","doi":"10.1007/s40818-022-00120-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove that the translating solitons of the mean curvature flow in <span>\\(\\mathbb {R}^4\\)</span> which arise as blow-up limit of embedded, mean convex mean curvature flow must have <i>SO</i>(2) symmetry.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"8 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"SO(2) Symmetry of the Translating Solitons of the Mean Curvature Flow in \\\\(\\\\mathbb {R}^4\\\\)\",\"authors\":\"Jingze Zhu\",\"doi\":\"10.1007/s40818-022-00120-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we prove that the translating solitons of the mean curvature flow in <span>\\\\(\\\\mathbb {R}^4\\\\)</span> which arise as blow-up limit of embedded, mean convex mean curvature flow must have <i>SO</i>(2) symmetry.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2022-03-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-022-00120-x\",\"RegionNum\":1,\"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":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-022-00120-x","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
SO(2) Symmetry of the Translating Solitons of the Mean Curvature Flow in \(\mathbb {R}^4\)
In this paper, we prove that the translating solitons of the mean curvature flow in \(\mathbb {R}^4\) which arise as blow-up limit of embedded, mean convex mean curvature flow must have SO(2) symmetry.
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