Andrew Zimmer, Louisiana State University
"Intrinsic and extrinsic geometries in several complex variables"
Despite being one of the simplest classes of manifolds, a bounded domain in complex Euclidean space has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the boundary is smooth, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will discuss how the infinitesimal and global curvature properties of the Kaehler-Einstein metric relate to classical conditions on the boundary like finite type and strong pseudoconvexity. Then, I will discuss how these relations motivate new analytic results for domains with non-smooth boundary.
M3 3103