Friday, November 30, 2018
3:00 PM -
5:00 PM
Linde Hall 187
Geometry and Topology Seminar
The geometry of domains with negatively pinched Kahler metrics
Every bounded pseudoconvex domain in C^n has a natural complete Kahler metric: the Kahler-Einstein metric constructed by Cheng-Yau. In this talk I will describe how the curvature of this metric restricts the CR-geometry of the boundary. In particular, I will sketch the proofs of the following two theorems: First, if a smoothly bounded convex domain has a complete Kahler metric with pinched negatively curved bisectional curvature, then the boundary of the domain has finite type in the sense of D'Angelo. Second, if a smoothly bounded convex domain has a complete Kahler metric with sufficiently tight pinched negatively curved holomorphic sectional curvature, then the boundary of the domain is strongly pseudoconvex. The proofs use recent results of Wu-Yau, classical results of Shi on the Ricci flow, and ideas from Benoist's work in real projective geometry. This is joint work with F. Bracci and H. Gaussier.
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