{"title":"封闭黎曼面上与特鲁丁格-莫泽函数相关的加权流","authors":"Peng Xiu Yu","doi":"10.1007/s10114-024-2447-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, with (Σ, <i>g</i>) being a closed Riemann surface, we analyze the possible concentration behavior of a heat flow related to the Trudinger-Moser energy. We obtain a long time existence for the flow. And along some sequence of times <i>t</i><sub><i>k</i></sub> → + ∞, we can deduce the convergence of the flow in <i>H</i><sup>2</sup>(Σ). Furthermore, the limit function is a critical point of the Trudinger-Moser functional under certain constraint.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 9","pages":"2244 - 2262"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Weighted Flow related to a Trudinger-Moser Functional on Closed Riemann Surface\",\"authors\":\"Peng Xiu Yu\",\"doi\":\"10.1007/s10114-024-2447-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, with (Σ, <i>g</i>) being a closed Riemann surface, we analyze the possible concentration behavior of a heat flow related to the Trudinger-Moser energy. We obtain a long time existence for the flow. And along some sequence of times <i>t</i><sub><i>k</i></sub> → + ∞, we can deduce the convergence of the flow in <i>H</i><sup>2</sup>(Σ). Furthermore, the limit function is a critical point of the Trudinger-Moser functional under certain constraint.</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":\"40 9\",\"pages\":\"2244 - 2262\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-20\",\"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/s10114-024-2447-0\",\"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/s10114-024-2447-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Weighted Flow related to a Trudinger-Moser Functional on Closed Riemann Surface
In this paper, with (Σ, g) being a closed Riemann surface, we analyze the possible concentration behavior of a heat flow related to the Trudinger-Moser energy. We obtain a long time existence for the flow. And along some sequence of times tk → + ∞, we can deduce the convergence of the flow in H2(Σ). Furthermore, the limit function is a critical point of the Trudinger-Moser functional under certain constraint.
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.
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