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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China(11971450)partially supported by the Project of Stable Support for Youth Team in Basic Research Field,CAS(YSBR-001)。
文摘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.
