报告题目：ON HOT SPOTS CONJECTURE FOR DOMAIN WITH N-AXES OF SYMMETRY

报 告 人：李亦教授（纽约城市大学）

报告时间：2025年9月26日  15:00

报告地点：格物楼528

报告摘要：

In this talk, we prove the hot spots conjecture for rotationally symmetric domains in R" by the conti-nuity method. More precisely, we show that the odd Neumann eigenfunction in x, associated withthe lowest nonzero eigenvalue is a Morse funetion on the boundary, which has exactly two criticalpoints and is monotone in the direction from its minimum point to its maximum point. As a consequence, we prove that the Jerison and Nadirashvili's conjecture 8.3 holds true for rotationally symmetric domains and are also able to obtain a sharp lower bound for the Neumann eigenvalue. We will also discuss some recent results on-axes symmetry or hyperbolic drum type domains.

报告人简介：

李亦教授是美国约翰·杰刑事司法学院教授，国际偏微分方程领域的知名专家。李亦教授于1988年获得美国明尼苏达大学博士学位，导师是倪维明教授。他的研究涉及非线性椭圆和抛物型偏微分方程及其相关应用，在Comm. Pure Appl. Math.、Duke Math. J.、Arch. Rational Mech. Ana1.等国际知名学术期刊上发表多篇论文。李亦教授曾担任美国爱荷华大学数学系主任、莱特州立大学科学与数学学院院长、加州州立大学北岭分校教务长兼学术事务副校长及约翰杰刑事司法学院教务长兼学术事务副校长，他于2018年当选为美国科学促进会（AAAS）会士并于2022年被授予约翰·杰学院总统学者（JJC Presidential Scholar）称号。