[吴文俊数学中心综合报告] Metrics of Eguchi-Hanson and Horowitz-Meyers Types and the Energy

We construct two types of Eguchi-Hanson metrics with the negative constant scalar curvature. The type I metrics are Kahler. The type II metrics are ALH whose total energy can be negative. We also construct a one-parameter family of complete metrics of Horowitz-Myers type with the negative constant scalar curvature, and verify a positive energy conjecture of Horowitz-Myers for these metrics. Furthermore, we prove the positive energy conjecture for a class of asymptotically Horowitz-Myers metrics on R2╳Tn-2, which generalizes the previous results of Barzegar-Chrusciel-Horzinger-Maliborski-Nguyen. The talk is based on the joint works with J. Chen and with Z. Liang.