Claremont Colleges Analysis Seminar
2007-2008

Title: A Green proof of Fatou’s theorem

Abstract:  Fatou’s theorem says that if a function is harmonic and bounded in the unit disk then it has non-tangential limits at almost every boundary point on the circle. By a conformal mapping the same kind of thing holds in a general simply connected domain if one considers, for example, limits along geodesics in the hyperbolic metric.

I’ll talk about how to prove statements like this without using the conformal mapping trick and where things can go wrong in multiply connected domains and in higher dimensions.