2015年几何暑期学校系列课程【Meijun Zhu】

授 课 人：Prof. Meijun Zhu (University of Okhlahoma，USA）

课程名称: Sharp Sobolev and HLS  inequalities and the applications

课程安排：6.24（星期三）6.26（星期五）14:00-16:00

地点：管理楼1418

Abstract: 

The first part of the course will cover Hardy inequality, Hardy-Littlewood-Sobolev inequality, Bliss lemma, symmetrization and Sharp Sobolev inequality on R^n;  the sharp Sobolev inequalities on compact manifolds and its application to the curvature equations. We mainly follow Aubin's original approach for solving the famous Yamabe equation. In the second part, we will discuss the sharp Hardy-Littlewood-Sobolev inequalities and the sharp reversed Hardy-Littlewood-Sobolev inequalities on R^n and compact manifolds. We then discuss the new approach for solving general Yamabe type problem based on the sharp HLS inequalities on compact manifolds.