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Mathematics Colloquium


Date:  Friday, September 19, 2008

Title:  Rigidity for holomorphic mappings of real hypersurfaces into hyperquadrics

Abstract:  The collection of holomorphic mappings of the complex plane sending a piece of the circle into itself is very large, infinite dimensional by any standard, and has no particularly interesting structure. In contrast, the collection of holomorphic mappings of complex 2-space sending a piece of the sphere into itself consists solely of automorphisms of the sphere and is hence, in particular, finite dimensional. This is a phenomenon that, when properly formulated, persists for holomorphic mappings sending a strictly pseudoconvex hypersurface into a sphere in a higher dimensional space, provided the difference in dimension is not too large. In this talk, we will describe this result, discuss an application to the study of isolated singularities, and explore what happens when pseudoconvexity is replaced by pseudoconcavity.

Speaker:  Peter Ebenfelt
Institution:  UCSD


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