报告题目：Uniqueness of critical points of the second Neumann eigenfunctions on triangles

报告摘要：In 1974, Rauch proposed the celebrated hot spots conjecture, asserting that the second Neumann eigenfunction attains its global extrema (the hottest and coldest points) exclusively on the boundary of the domain. Notably, for triangular domains T, the absence of interior critical points was recently established by Judge and Mondal (Ann. Math. (2) 195(1):337–362, 2022). In this talk, we will present a complete resolution of several important questions about the second Neumann eigenfunction on triangles. Our proofs combine the continuity method, eigenvalue inequalities, the maximum principle, and the moving plane method. This is a joint work with Prof. Hongbin Chen(XJTU) and Prof. ChangfengGui (UM).

报告人简介：姚若飞，西安交通大学博士，中南大学博士后。2020年12月入职华南理工大学，现任教授。主要研究方向为偏微分方程理论，尤其关注热点猜想以及椭圆型偏微分方程解的对称性与单调性问题。相关成果发表于 Calc. Var. Partial Differential Equations、Invent. Math.、J. Differential Equations、J. Funct. Anal.、Math. Ann.、Nonlinearity、SIAM J. Math. Anal. 等国际期刊。

报告时间：2026年04月01日 16:00-17:00

报告地点：武之楼412会议室