报告题目：Uniqueness of blowup solutions and non-degeneracy of singular Liouville equation

报告时间：2025-01-13   09:00-10:00

报  告 人 ：张雷   教授（佛罗里达大学）

线上报告：Zoom，880 3779 2918  密码，987971

Abstract：For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions if blowup points are either regular points or non-quantized singular sources. The uniqueness result covers the most general case extending or improving all previous works. In addition, we also establish the nondegeneracy of the singular Liouville equation. 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 created several new estimates of independent interest about the concentration phenomenon for Liouville-type equations. This talk is based on joint works with D. Bartolucciand W. Yang.