Abstract

Classical work by W.~Blaschke (1915) and F.Riesz (1920's) gives a complete description of the zero sets of all bounded analytic functions in the open unit disk. This has important ramifications in real analysis, functional analysis and operator theory. In 1961  M.~Heins raised the problem to give a characterization of the critical sets of bounded analytic functions instead of the zero sets. Understanding the critical points of analytic functions in general plays a crucial role e.g.~in complex dynamics or discrete analytic function theory.

The aim of this talk is to discuss a complete characterization of the critical sets of bounded analytic functions. Our approach is based on techniques from several areas of geometric analysis such as Complex Analysis (Bergman spaces, BMOA), PDEs (Gaussian curvature equation) and Conformal Geometry (conformal Riemannian metrics). A main step consists in providing a partial solution to the Berger--Nirenberg problem from Differential Geometry

Tee/Kaffee/Gebäck

ab  16:45 Uhr,

Arnimallee 3,  Raum 006

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Koordinator:  Prof. Dr. Alexander Schmitt

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