Semicontinuity of the Automorphism Groups of Domains with Rough Boundary

Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in \CC^n, $n > 1$, with Lipschitz boundary, but it holds for domains in \CC^1 with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitz domains. These include Bergman curvature, stability properties for the Bergman kernel, and also some ideas about equivariant embeddings

The corona problem with two pieces of data

We study the corona problem on the unit ball in \CC^n, and more generally on strongly pseudoconvex domains in \CC^n. When the corona problem has just two pieces of data, and an extra geometric hypothesis is satisfied, then we are able to solve it

On Limits of Sequences of Holomorphic Functions

We study functions which are the pointwise limit of a sequence of holomorphic functions. In one complex variable this is a classical topic, though we offer some new points of view and new results. Some novel results for solutions of elliptic equations will be treated. In several complex variables the question seems to be new, and we explore some new avenues.Comment: one figur