For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions if some blowup points coincide with the singularities of the Dirac data. If the strength of the Dirac mass at each blowup point is not a multiple of 4π, we prove that bubbling solutions are unique. This paper extends previous results of Lin-Yan [C. S. Lin and S. S. Yan, On the mean field type bubbling solutions for Chern–Simons–Higgs equation, Adv. Math. 338 (2018) 1141–1188] and Bartolucci et al. [D. Bartolucci, A. Jevnikar, Y. Lee and W. Yang, Uniqueness of bubbling solutions of mean field equations, J. Math. Pures Appl. (9) 123 (2019) 78–126].

中文翻译：

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具有非量化奇点的平均场方程冒泡解的唯一性

对于定义在紧黎曼曲面上的奇异平均场方程，如果某些爆破点与狄拉克数据的奇异点重合，我们证明了冒泡解的唯一性。如果每个爆发点的狄拉克质量的强度不是4π，我们证明冒泡解决方案是唯一的。本文扩展了 Lin-Yan 先前的结果 [CS Lin 和 SS Yan，关于 Chern-Simons-Higgs 方程的平均场型冒泡解，进阶。数学。 338(2018) 1141–1188] 和 Bartolucci 等人。[D。Bartolucci、A. Jevnikar、Y. Lee 和 W. Yang，平均场方程冒泡解的唯一性，J.数学。纯应用程序。 (9) 123(2019) 78–126]。