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Journal of University of Chinese Academy of Sciences ›› 2025, Vol. 42 ›› Issue (5): 589-599.DOI: 10.7523/j.ucas.2023.091

• Research Articles • Previous Articles    

Some analytic results and applications in extremal Hermitian metrics

SANG Haoxin, WU Yingyi   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
  • Received:2023-10-07 Revised:2023-12-20
  • Contact: WU Yingyi, E-mail: wuyy@ucas.ac.cn
  • Supported by:
    Supported by the National Natural Science Foundation of China (11971450) and partially supported by the Project of Stable Support for Youth Team in Basic Research Field, CAS (YSBR-001)

Abstract: 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.

Key words: extremal Hermitian metrics, conical singularities of metrics, Newtonian potential

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