2013年几何学暑期学校短期课程

课程题目：Introduction to local regularity problems of Ricci flow
授课人：Prof. Qi Zhang （University of California Riverside）                                                                   课时安排：  7月26日  16:00-18:00  

           7月30日  10:00-12:00    

           8月3日   10:00-12:00    15:00-17:00

           8月5日、7日  9:00-11:00
授课地点： 管理科研楼1218

课程摘要：

This is intended to be an introductory topic course for graduate students/young researchers with some background of Ricci flow. We will start with Perelman's volume lower bound of geodesic balls, which is also known as the Kappa non-collapsing property. Then we will discuss the opposite result namely the volume upper bound, also known as the Kappa noninflating property. Next topics are the Sobolev inequality, isoperimetric and Poincar/'e inequalities in Ricci flow, especially Kaehler Ricci flow . These properties allow one to carry out some analysis of curvature equations, such as /epsilon regularity. We will also describe some difficulties and potential problems and their relations with the convergence issue of Kaehler Ricci flow, such as the recent work of Professor Tian Gang and coauthors and Professor Chen xiuxiong-Wang Bing.