Fourier analysis on hyperbolic spaces and sharp geometric inequalities

      Geometric inequalities have important applications in modern analysis, differential geometry and partial differential equations. In this talk, we will report some works on sharp Hardy-Sobolev-Mazya inequalities and their borderline case Hardy-Trudinger -Moser and Hardy-Adams inequalities. Fourier analysis on hyperbolic spaces play an important role in establishing these inequalities.
      These are joint work with Jungang Li, and Qiaohua Yang.