介绍并证明了3个分析中的结果, 分别是函数的一致收敛、Newtonian位势的基本性质以及一种Sobolev空间中受函数列Laplacian算子控制的收敛。随后利用前述分析中的结果, 给出Guofang Wang和Xiaohua Zhu一项分类结果中出现的一处重要估计的完整证明, 该结果阐述了紧Riemann曲面上能量和面积有限且带有有限个较小角度奇点的极值Hermitian度量的分类。
In this paper, we introduce and prove three analytic results related to uniform convergence, properties of Newtonian potential, and convergence of sequences in Sobolev space constrained by their Laplacian. Then, utilizing our analytic results, we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu, which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.
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