Analysis and Geometric Analysis Seminar
n this talk, we will discuss 4-dimensional gradient shrinking Ricci solitons. In the first part, we will present some curvature estimates for 4-dimensional complete gradient Ricci solitons (joint work with H.-D. Cao and D. Zhou). In the second part, we will show that, under an upper bound condition on the range of the potential function, a 4-dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality (joint work with X. Cheng and D. Zhou). Some open problems will also be discussed.