8 citations · 29 across the 22 of their papers we have counts for
6 papers · 1 filter
Carathéodory's Theorem and moduli of local connectivity
Timothy H. McNicholl
We give a constructive proof of the Carathéodory Theorem by means of the concept of a modulus of local connectivity and the extremal distance of the separating curves of an annulus…
Computing conformal maps onto circular domains
Valentin V. Andreev, Dale Daniel, Timothy H. McNicholl
We show that, given a non-degenerate, finitely connected domain , its boundary, and the number of its boundary components, it is possible to compute a conformal mapping of o…
Computing boundary extensions of conformal maps part 2
T. H. McNicholl
It is shown that there is a computable conformal map of the unit disk onto a domain that has a computable extension to the closure of the unit disk even though the boundary of…
An operator-theoretic existence proof of solutions to planar Dirichlét problems
Timothy H. McNicholl
By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichlét problems for planar Jordan domains with at least two…
Computing boundary extensions of conformal maps
Timothy H. McNicholl
Let be a conformal map of the unit disk onto a domain , and suppose has a boundary extension. We show that arbitrarily good approximations of the boundary extension of $…
An effective Caratheodory Theorem
Timothy H. McNicholl
By means of the property of effective local connectivity, the computability of finding the Carathéodory extension of a conformal map of a Jordan domain onto the unit disk is demons…