Sharp geometric inequalities--Their proofs and applications
主 题: Sharp geometric inequalities--Their proofs and applications
报告人: 陆国震 教授 (北京师范大学, 美国韦恩州立大学)
时 间: 2011-12-09 14:00-15:00
地 点: 理科一号楼1114 （数学所活动）
In this talk we will discuss a number of well known geometric inequalities such as Poincare and Sobolev inequalities, isoperimetric inequalities, Moser-Trudinger inequalities, Hardy-Littlewood-Sobolev inequalities, etc in various settings including the Euclidean space, Heisenberg group, Carnot-Carathedory spaces, Riemannian manifolds and sub-Riemannian manifolds, etc. Their proofs largely use some basic techniques in harmonic analysis such as representation formulas, fractional integral estimates, covering lemmas, etc. These inequalities in sharp forms are important in geometry and partial differential equations. This talk aims for general audience and therefore technical details will be avoided.