The converse of Cauchy’s theorem for arbitrary Riemann surfaces
Author:
Myron Goldstein
Journal:
Proc. Amer. Math. Soc. 25 (1970), 177-178
MSC:
Primary 30.45
DOI:
https://doi.org/10.1090/S0002-9939-1970-0257345-9
MathSciNet review:
0257345
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we prove a generalization of the converse of Cauchy’s theorem which is valid for arbitrary hyperbolic Riemann surfaces. The tools used are the Kuramochi compactification and the concept of generalized normal component.
- Lars V. Ahlfors and Leo Sario, Riemann surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J., 1960. MR 0114911
- Corneliu Constantinescu and Aurel Cornea, Ideale Ränder Riemannscher Flächen, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 32, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963 (German). MR 0159935
- H. L. Royden, The boundary values of analytic and harmonic functions, Math. Z. 78 (1962), 1–24. MR 138747, DOI https://doi.org/10.1007/BF01195147
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Additional Information
Keywords:
Normal component,
quasicontinuous extension,
analytic differentials,
regular point,
Kuramochi compactification
Article copyright:
© Copyright 1970
American Mathematical Society