A remark on the prolongation of Riemann surfaces of finite genus

Akira MORI

doi:10.2969/jmsj/00410027

Akira MORI

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1952 Volume 4 Issue 1 Pages 27-30

DOI https://doi.org/10.2969/jmsj/00410027

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Published: 1952 Received: April 27, 1951 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) L. Sario: Über Riemannsche Flächen mit hebbarem Rand, Ann. Acad. Sci. Fennicae A. I. Nr. 50 (1948).
2) S. Bochner: Fortsetzung Riemannscher Flächen, Math. Ann. 98 (1928). L. Sario: loc. cit. Also our argument in this note contains a proof of the possibility of such mappings.
3) R. Nevanlinna: Eindeutigkeitsfragen in der Theorie der konformen Abbildung. 10. Congr. Math. Scand. Copenhagen 1946.
4) L. Ahlfors and A. Beurling: Conformal invariants and function-theoretic null-sets, Acta Math. 83 (1950), Theorem 6.
5) Ahlfors-Beurling: loc. cit. The equivalency of our definition with theirs is shown by Theorem 5 there or by the Lemma in this note.
6) L. Sario: loc. cit. Ahlfors-Beurling: loc. cit., Theorem 5.
7) C. Neumann: Abelsche Integrale, 2. Aufl. 1884. W. F. Osgood: Lehrbuch der Funktionentheorie II, 2, Kap. 5.

Right : 1) L. Sario: Über Riemannsche Flächen mit hebbarem Rand, Ann. Acad. Sci. Fennicae A. I. Nr. 50 (1948).
2) S. Bochner: Fortsetzung Riemannscher Flächen, Math. Ann. 98 (1928). L. Sario: loc. cit. Also our argument in this note contains a proof of the possibility of such mappings.
3) R. Nevanlinna: Eindeutigkeitsfragen in der Theorie der konformen Abbildung. 10. Congr. Math. Scand. Copenhagen 1946.
4) L. Ahlfors and A. Beurling: Conformal invariants and function-theoretic nullsets, Acta Math. 83 (1950), Theorem 6.
5) Ahlfors-Beurling: loc. cit. The equivalency of our definition with theirs is shown by Theorem 5 there or by the Lemma in this note.
6) L. Sario: loc. cit. Ahlfors-Beurling: loc. cit, Theorem 5.
7) C. Neumann: Abelsche Integrale, 2. Aufl. 1884. W. F. Osgood: Lehrbuch der Funktionentheorie II, 2, Kap. 5.

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