Helgason-Fourier analysis techniques in sharp geometric inequalities on hyperbolic spaces

Abstract: In recent years, we have developed a new approach to establish sharp geometric and functional inequalities using the Helgason-Fourier analysis techniques on symmetric spaces. Such inequalities include sharp higher order Hardy-Sobolev-Maz'ya and Hardy-Adams inequalities on hyperbolic spaces on all Riemannian symmetric spaces of noncompact type of rank one. Precise expressions of Green's functions of GJMS operators on real hyperbolic spaces in terms of hypergeometric functions are established as well.This is based on a series of joint works with Joshua Flynn, Jungang Li, and Qiaohua Yang.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php