The role of Fourier analysis on hyperbolic spaces in sharp geometric inequalities

题目：The role of Fourier analysis on hyperbolic spaces in sharp geometric inequalities

报告人: 陆国震教授，美国康涅狄格大学

地点：玉泉校区工商楼200-9

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 hperbolic 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.