Abstract. 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.

Bio. 张晓，广西数学中心教授、执行主任，中科院数学研究所研究员，曾获国家杰出青年基金资助，入选中国科学院“百人计划”，广西壮族自治区八桂学者和广西大学君武学者。研究方向为微分几何与数学物理，在广义相对论正能量问题及引力量子化的非交换几何理论上做出了重要贡献。