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).
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Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ23A010001)
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Fang, Y., Yang, Y.Y. Trudinger–Moser Inequalities on a Closed Riemann Surface with a Symmetric Conical Metric. Acta. Math. Sin.-English Ser. 40, 2263–2284 (2024). https://doi.org/10.1007/s10114-024-2566-7
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DOI: https://doi.org/10.1007/s10114-024-2566-7