题目：Compactness of asymptotically hyperbolic Einstein 4-manifolds
Abstract: Let X be a differential 4-manifold with the boundary M =∂X. Given a conformal class (M, [h]) of Riemannian metric h on M, we try to find“conformal filling in” a asymptotically hyperbolic Einstein g_+ on X such that r^2 g_+|M = h for some defining function r on X. The study of complete AH Einstein manifolds has become very active due to the AdS/CFT correspondence in string theory.
In this talk, instead of addressing the existence problem of a conformal filling in, we discuss the compactness problem, that is, how the compactness of the sequence of conformal infinity metrics leads to the compactness result of the compactified filling in AHE manifolds under the suitable assumptions on the topology of X and some conformal invariants. We briefly survey some known results then report recent joint work in progress with Alice Chang. Some applications will be discussed.
报告人简介：葛宇新，法国图卢兹三大教授，研究方向为微分几何、偏微分方程。近几年，在四维爱因斯坦流形的紧性问题上做出了重要贡献。在Comm. Pure Appl. Math., J. Diff. Geom., Adv. Math., J. Funct. Anal.等国际著名数学期刊中发表学术论文50多篇。