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.

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