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2005•Complex Variables Theory and Application An International JournalRequires access

Two results on uniqueness of conformal mappings

Steven G. Krantz

Open publisher page 3 citations

Abstract

In this article, we give new, elementary, and very geometric proofs of two results in conformal mapping theory. One of these – about the size of the isotropy group of the set of conformal mappings of a domain – is nearly three-quarters of a century old. The other – about fixed points – is just two decades old.

About this research paper

What this paper is about

In this article, we give new, elementary, and very geometric proofs of two results in conformal mapping theory. One of these – about the size of the isotropy group of the set of conformal mappings of a domain – is nearly three-quarters of a century old. The other – about fixed points – is just two decades old.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this article, we give new, elementary, and very geometric proofs of two results in conformal mapping theory. One of these – about the size of the isotropy group of the set of conformal mappings of a domain – is nearly three-quarters of a century old. The other – about fixed points – is just two decades old.

Key concepts: Conformal map, Extremal length, Mathematics, Uniqueness, Mathematical proof, Isotropy, Set (abstract data type), Pure mathematics

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