学术报告：具有有界Ricci曲率流形的L2曲率界

中科院数学与系统科学研究院

数学研究所

调和分析及其应用中心

学术报告会

报告人：    江文帅（北京大学）

题  目：具有有界Ricci曲率流形的L²曲率界

时  间：2016.06.02 (星期四), 15:00--17:00

地  点：数学院南楼N913室

Abstract:

In this talk, we will discuss the L² curvature estimates on manifolds with bounded Ricci curvature and noncollapsing volume. Firstly, we will talk about the background, then we introduce the concept of neck region which appears everywhere in our proof. After that, we would sketch the whole proofs. 

At last, we would focus on the technical details and our new observations on neck region. One is the local L² curvature estimate on the regular ball with harmonic radius lower bound.  The other key new ingredient is a superconvexity estimates of the hessian of harmonic functions. All the estimates are on neck region. This is joint work with Prof. Aaron Naber.