{"title":"Trudinger–Moser Inequalities on a Closed Riemann Surface with a Symmetric Conical Metric","authors":"Yu Fang, Yun Yan Yang","doi":"10.1007/s10114-024-2566-7","DOIUrl":null,"url":null,"abstract":"<div><p>This is a continuation of our previous work (<i>Ann. Sc. Norm. Super. Pisa Cl. Sci.</i>, <b>20</b>, 1295–1324, 2020). Let (Σ, <i>g</i>) be a closed Riemann surface, where the metric <i>g</i> has conical singularities at finite points. Suppose <b>G</b> is a group whose elements are isometries acting on (Σ, <i>g</i>). Trudinger–Moser inequalities involving <b>G</b> are established via the method of blow-up analysis, and the corresponding extremals are also obtained. This extends previous results of Chen (<i>Proc. Amer. Math. Soc.</i>, 1990), Iula–Manicini (<i>Nonlinear Anal.</i>, 2017), and the authors (2020).</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 9","pages":"2263 - 2284"},"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/s10114-024-2566-7","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
Abstract
This is a continuation of our previous work (Ann. Sc. Norm. Super. Pisa Cl. Sci., 20, 1295–1324, 2020). Let (Σ, g) be a closed Riemann surface, where the metric g has conical singularities at finite points. Suppose G is a group whose elements are isometries acting on (Σ, g). Trudinger–Moser inequalities involving G are established via the method of blow-up analysis, and the corresponding extremals are also obtained. This extends previous results of Chen (Proc. Amer. Math. Soc., 1990), Iula–Manicini (Nonlinear Anal., 2017), and the authors (2020).
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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