5月27日下午4点--Fourier analysis on hyperbolic spaces and sharp geometric inequalities
报告人：Prof. Guozhen Lu
University of Connecticut
题 目：Fourier analysis on hyperbolic spaces and sharp geometric inequalities
摘 要：Sharp geometric inequalities play an important role in analysis and differential geometry. In this talk, we will review some recent works on sharp Hardy-Sobolev-Maz'ya inequalities on the upper half space which improve the classical Sobolev inequality. We will also discuss the borderline case of the Sobolev inequalities, namely, the Trudinger-Moser and Adams inequalities on hyperbolic spaces. In particular, we will describe the Fourier analysis techniques on the hyperbolic spaces and their applications to establish sharp geometric inequalities and prove that the best constants for the Hardy-Sobolev-Maz'ya and Sobolev inequalities are the same in some cases and are different in other cases.