2011•arXiv (Cornell University)Open access

AN ALGORITHM FOR COMPUTING BOUNDARY EXTENSIONS OF CONFORMAL MAPS

Timothy H. McNicholl

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Abstract

We show that from a sufficiently good approximation to a con- formal map of the unit disk onto a bounded domain D, a sufficiently good approximation to the boundary of D, and sufficient local connectivity infor- mation for @D, it is possible to compute arbitrarily good approximations to the boundary extension of �.

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What this paper is about

We show that from a sufficiently good approximation to a con- formal map of the unit disk onto a bounded domain D, a sufficiently good approximation to the boundary of D, and sufficient local connectivity infor- mation for @D, it is possible to compute arbitrarily good approximations to the boundary extension of �.

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Available abstract

We show that from a sufficiently good approximation to a con- formal map of the unit disk onto a bounded domain D, a sufficiently good approximation to the boundary of D, and sufficient local connectivity infor- mation for @D, it is possible to compute arbitrarily good approximations to the boundary extension of �.

Key concepts: Boundary (topology), Conformal map, Bounded function, Extension (predicate logic), Unit disk, Domain (mathematical analysis), Mathematics, Unit (ring theory)

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