Shenzhen University School of Mathematical Sciences  

Liyuan Scholars Colloquium Session 176

Title: Some New Inequalities In Analysis And Geometry

Speaker: Professor Changfeng Gui (Carnegie Mellon University)

Time: 10:30–11:30, June 22, 2026

Location: Room 2, Huixing Building, Yuehai Campus, Shenzhen University

Abstract:  The classical Moser-Trudinger inequality is a borderline case of Sobolev inequalities and plays an important role in geometric analysis and PDEs in general. Aubin in 1979 showed that the best constant 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 the sphere 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.

Speaker Profile: Changfeng Gui is a Chair Professor at the Faculty of Science and Technology and Chair of the Department of Mathematics at the University of Macau, as well as a Distinguished Mathematics Scholar Professor at the University of Macau Development Foundation. He previously served as an Assistant Professor and Associate Professor at the University of British Columbia in Canada, a Professor at the University of Connecticut in the United States, and the Dan Palman Endowed Chair in Applied Mathematics at the University of Texas at San Antonio. His research focuses on nonlinear partial differential equations, image analysis, and image processing. He has published numerous papers in top-tier international journals such as Annals of Mathematics, Inventiones Mathematicae, and Communications on Pure and Applied Mathematics. He has received awards including the Research Achievement Award from the Pacific Institute for the Mathematics of Canada, the Aisensdadt Award from the Canadian Centre for Mathematics, the Best Paper Award from the IEEE Signal Processing Society, and the Overseas Cooperation Fund (Overseas Outstanding Young Scientist) from the National Natural Science Foundation of China. He has been selected as a Changjiang Scholar Chair Professor by the Ministry of Education and as a National Distinguished Expert. He is a Fellow of the American Mathematical Society (first class), a Fellow of the Simmons Society, and a Fellow of the American Association for the Advancement of Science (AAAS).

All faculty and students are welcome!  

School of Mathematical Sciences  

June 20, 2026