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<p>For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions provided the blowup points are either regular or non-quantized singular sources. In particular, the uniqueness result covers the most general case, extending and improving all previous works of Bartolucci–Jevnikar–Lee–Yang [<CitationRef CitationID="CR17">17</CitationRef>, <CitationRef CitationID="CR21">21</CitationRef>] and Wu–Zhang [<CitationRef CitationID="CR81">81</CitationRef>]. For example, unlike previous results, we drop the assumption that singular sources are critical points of a suitably defined Kirchhoff–Routh type functional. Our argument is based on refined estimates, robust and flexible enough to be applied to a wide range of problems requiring a delicate blowup analysis. In particular, we present several new estimates of independent interest regarding the concentration phenomenon for Liouville-type equations.</p>

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Asymptotic analysis and uniqueness of blowup solutions of non-quantized singular mean field equations

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Daniele Bartolucci,
  • Wen Yang,
  • Lei Zhang

摘要

For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions provided the blowup points are either regular or non-quantized singular sources. In particular, the uniqueness result covers the most general case, extending and improving all previous works of Bartolucci–Jevnikar–Lee–Yang [17, 21] and Wu–Zhang [81]. For example, unlike previous results, we drop the assumption that singular sources are critical points of a suitably defined Kirchhoff–Routh type functional. Our argument is based on refined estimates, robust and flexible enough to be applied to a wide range of problems requiring a delicate blowup analysis. In particular, we present several new estimates of independent interest regarding the concentration phenomenon for Liouville-type equations.