Pak-Yeung Chan (University of Warwick)

Gap theorem for nonnegatively curved manifolds

Abstract: In this seminar, we shall discuss some recent results 
on the gap theorem of nonnegatively curved manifolds with small 
curvature in an average integral sense, which can be viewed as 
a Riemannian analogue of the optimal gap result by Ni on Kaehler manifolds. 
In dimension 3, we also establish a gap theorem for Ricci nonnegative 
manifolds with pointwise quadratic curvature decay and fast average 
integral curvature decay. 

This talk is based on some joint works with Man-Chun Lee.