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Complex Analysis and Geometry Seminar

The geometry of domains with negatively pinched Kaehler metrics

Andrew Zimmer, Louisiana State University, Baton Rouge

Location:  Hill 705
Date & time: Friday, 15 March 2019 at 10:30AM - 11:30AM

Abstract. Every bounded pseudoconvex domain in CnCn has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex.

This is joint work with F. Bracci and H. Gaussier.