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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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: 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.


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Keywords: Normal component, quasicontinuous extension, analytic differentials, regular point, Kuramochi compactification
Article copyright: © Copyright 1970 American Mathematical Society