Conformal mapping of regions bounded by curvilinear polygons
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- by Burton Rodin
- Proc. Amer. Math. Soc. 94 (1985), 297-300
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784182-X
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Abstract:
The main result is the proof that, under a natural notion of conformal equivalence, any curvilinear polygon is conformally equivalent to a curvilinear polygon whose inside region is starlike. The method of proof is a new type of continuity argument which, in distinction to the classical continuity method, yields existence without requiring uniqueness.References
- R. Courant, Über eine Eigenschaft der Abbildungsfunktionen bei konformer Abbildung, Nachrichten von der Gesellschaft der Wissenschaften, Göttingen, 1914, pp. 101-109.
—, Bemerkung zu meiner Arbeit: "Über eine Eigenschaft...", Nachrichten von der Gesellschaft der Wissenschaften, Göttingen, 1922, pp. 69-70.
- G. M. Goluzin, Geometric theory of functions of a complex variable, Translations of Mathematical Monographs, Vol. 26, American Mathematical Society, Providence, R.I., 1969. MR 0247039 T. Radó, Sur la représentation conforme des domaines variables, Acta Litt. Sci. Univ. Francisco-Josephinae 1 (1923), 180-186.
- M. Tsuji, Potential theory in modern function theory, Maruzen Co. Ltd., Tokyo, 1959. MR 0114894
- James W. Vick, Homology theory, Pure and Applied Mathematics, Vol. 53, Academic Press, New York-London, 1973. An introduction to algebraic topology. MR 0375279
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 297-300
- MSC: Primary 30C20
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784182-X
- MathSciNet review: 784182