报告题目：Some New Inequalities In Analysis And Geometry
时 间：2026年06月04日（星期四）9：10
地 点：理工南楼201
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和学生
报告摘要：The classical Moser-Trudinger inequality is a borderline case of Sobolev inequalities and plays animportant role in geometric analysis and PDEs in general. Aubin in 1979 showed that the bestconstant in the Moser-Trudinger inequality can be improved by reducing to one half if the functions are restricted to the complement of a three dimensional subspace of the Sobolev space H1, while Onofri in 1982 discovered an elegant optimal form of Moser-Trudinger inequality on sphere. In this talk, I will present new sharp inequalities which are variants of Aubin and Onofri inequalities on thesphere with or without mass center constraints. Efforts have also been made to show similar inequalities in higher dimensions. We have improved Beckner’s inequality, the higher dimensional counterpart of Onofri’s inequality, for axially symmetric functions when the dimension n = 4, 6, 8. Numerical computations are exploited to provide rigorous proof.I will also present some new results on higher dimensional counterpart of Huber’s isoperimetric inequalities.
报告人简介：桂长峰，澳门大学科技学院讲座教授、数学系主任，澳大发展基金会数学杰出学人教授，曾任加拿大英属哥伦比亚大学助理教授， 副教授，美国康涅狄格大学教授，美国德州大学圣安东尼奥分校丹．帕尔曼应用数学冠名讲座教授。研究方向为非线性偏微分方程、图像分析和处理，解决了众多世界数学难题，在国际顶级期刊如《Annals of Mathematics》《Inventiones Mathematicae》《Communications on Pure and Applied Mathematics》等发表近百篇论文。曾获颁加拿大太平洋数学研究所研究成果奖、加拿大数学中心Aisensdadt 奖、IEEE信号处理协会最佳论文奖、中国国家自然科学基金海外合作基金（海外杰青）等奖项。入选国家级高层次人才计划。是美国数学学会首届会士、美国西蒙斯会士、美国科学促进会（AAAS）会士。