Unicity theorems for the Gauss maps of complete minimal surfaces

Hirotaka FUJIMOTO

doi:10.2969/jmsj/04530481

Hirotaka FUJIMOTO

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JOURNAL FREE ACCESS

1993 Volume 45 Issue 3 Pages 481-487

DOI https://doi.org/10.2969/jmsj/04530481

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Published: 1993 Received: June 19, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Shoshichi Kobayashi on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) L. V. Ahlfors, An extension of Schwarz's lemma, Trans. Amer. Math. Soc., 43 (1938), 359-364.
2) S. S. Chern and R. Osserman, Complete minimal surfaces in euclidean n-space, J. Analyse Math., 19 (1967), 15-34.
3) O. Forster, Lectures on Riemann surfaces, Springer-Verlag, Berlin-Heidelberg-New York, 1981.
4) H. Fujimoto, A unicity theorem for meromorphic maps of a complete Kähler manifold into P^N(C), Tohoku Math. J., 38 (1986), 327-341.
5) H. Fujimoto, On the number of exceptional values of the Gauss map of minimal surfaces, J. Math. Soc. Japan, 40 (1988), 235-247.
6) H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, J. Differential Geom., 29 (1989), 245-262.
7) H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, II, J. Differential Geom., 31 (1990), 365-385.
8) H. Fujimoto, On the Gauss curvature of minimal surfaces, J. Math. Soc. Japan., 44 (1992), 427-439.
9) R. Nevanlinna, Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen, Acta Math., 48 (1926), 367-391.
10) R. Osserman, Global properties of minimal surfaces in E³ and Eⁿ, Ann. of Math., 80 (1964), 340-364.
11) R. Osserman, A survey of minimal surfaces, 2nd ed., Dover Publ. Inc., New York, 1986.

Right : [1] L. V. Ahlfors, An extension of Schwarz's lemma, Trans. Amer. Math. Soc., 43 (1938), 359-364.
[2] S. S. Chern and R. Osserman, Complete minimal surfaces in euclidean n-space, J. Analyse Math., 19 (1967), 15-34.
[3] O. Forster, Lectures on Riemann surfaces, Springer-Verlag, Berlin-Heidelberg-New York, 1981.
[4] H. Fujimoto, A unicity theorem for meromorphic maps of a complete Kähler manifold into P^N(C), Tôhoku Math. J., 38 (1986), 327-341.
[5] H. Fujimoto, On the number of exceptional values of the Gauss map of minimal surfaces, J. Math. Soc. Japan, 40 (1988), 235-247.
[6] H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, J. Differential Geom., 29 (1989), 245-262.
[7] H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, II, J. Differential Geom., 31 (1990), 365-385.
[8] H. Fujimoto, On the Gauss curvature of minimal surfaces, J. Math. Soc. Japan., 44 (1992), 427-439.
[9] R. Nevanlinna, Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen, Acta Math., 48 (1926), 367-391.
[10] R. Osserman, Global properties of minimal surfaces in E³ and Eⁿ, Ann. of Math., 80 (1964), 340-364.
[11] R. Osserman, A survey of minimal surfaces, 2nd ed., Dover Publ. Inc., New York, 1986.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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