{"title":"凸超曲面的非均质完全非线性收缩流","authors":"Pengfei Guan, Jiuzhou Huang, Jiawei Liu","doi":"10.1515/ans-2022-0077","DOIUrl":null,"url":null,"abstract":"We consider a general class of non-homogeneous contracting flows of convex hypersurfaces in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> <jats:tex-math> ${\\mathbb{R}}^{n+1}$ </jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_ans-2022-0077_ineq_001.png\" /> </jats:alternatives> </jats:inline-formula>, and prove the existence and regularity of the flow before extincting to a point in finite time.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"22 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-homogeneous fully nonlinear contracting flows of convex hypersurfaces\",\"authors\":\"Pengfei Guan, Jiuzhou Huang, Jiawei Liu\",\"doi\":\"10.1515/ans-2022-0077\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a general class of non-homogeneous contracting flows of convex hypersurfaces in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\" overflow=\\\"scroll\\\"> <m:msup> <m:mrow> <m:mi mathvariant=\\\"double-struck\\\">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> <jats:tex-math> ${\\\\mathbb{R}}^{n+1}$ </jats:tex-math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_ans-2022-0077_ineq_001.png\\\" /> </jats:alternatives> </jats:inline-formula>, and prove the existence and regularity of the flow before extincting to a point in finite time.\",\"PeriodicalId\":7191,\"journal\":{\"name\":\"Advanced Nonlinear Studies\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advanced Nonlinear Studies\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ans-2022-0077\",\"RegionNum\":2,\"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":"Advanced Nonlinear Studies","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ans-2022-0077","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们考虑了 R n + 1 ${{mathbb{R}}^{n+1}$ 中凸超曲面的一类非均质收缩流，并证明了流在有限时间内消亡到某一点之前的存在性和正则性。
Non-homogeneous fully nonlinear contracting flows of convex hypersurfaces
We consider a general class of non-homogeneous contracting flows of convex hypersurfaces in Rn+1 ${\mathbb{R}}^{n+1}$ , and prove the existence and regularity of the flow before extincting to a point in finite time.
期刊介绍：
Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.
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