Ahlfors Maps, the Double of a Domain, and Complexity in Potential Theory and Conformal Mapping
نویسنده
چکیده
We prove that the Bergman kernel function associated to a finitely connected planar domain can be expressed as a rational combination of two independent Ahlfors maps associated to the domain plus the derivative of one of the maps. Similar results are shown to hold for the Szegő and Poisson kernels and other objects of potential theory. These results generalize routinely to the case of a relatively compact domain in a Riemann surface with finitely many boundary components.
منابع مشابه
The Ahlfors Iteration for Conformal Mapping A
of the Dissertation The Ahlfors Iteration for Conformal Mapping by Christopher Michael Green Doctor of Philosophy in Mathematics Stony Brook University 2011 The Riemann Mapping Theorem states that for any proper, simply connected planar domain there exists a conformal mapping from the disk onto the domain. But can this map be explicitly described? For general domains, there is no obvious answer...
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