On the number of exceptional values of the Gauss maps of minimal surfaces

Hirotaka FUJIMOTO

doi:10.2969/jmsj/04020235

Hirotaka FUJIMOTO

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JOURNAL FREE ACCESS

1988 Volume 40 Issue 2 Pages 235-247

DOI https://doi.org/10.2969/jmsj/04020235

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Published: 1988 Received: May 09, 1986 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: CITATION Details: Wrong : 1) L.A. Ahlfors, Conformal invariants, Topics in geometric function theory, McGraw-Hill, New York, 1973.
2) C. C. Chen, On the image of the generalized Gauss map of a complete minimal surface in R⁴, Pacific J. Math., 102 (1982), 9-14.
3) S. S. Chern and R. Osserman, Complete minimal surfaces in euclidean n-space, J. Analyse Math., 19 (1967), 15-34.
4) H. Fujimoto, On the Gauss map of a complete minimal surface in R^m, J. Math. Soc. Japan, 35 (1983), 279-288.
5) H. Fujimoto, Value distribution of the Gauss maps of complete minimal surfaces in R^m, J. Math. Soc. Japan, 35 (1983), 663-681.
6) H. Fujimoto, Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into P^N₁(C)×...×P^N_k(C), Japanese J. Math., 11(1985), 233-264.
7) R. Narasimhan, Complex analysis in one variable, Birkhäuser, Boston, 1985.
8) R. Osserman, Minimal surfaces in the large, Comment. Math. Helv., 35 (1961), 65-76.
9) R. Osserman, Global properties of minimal surfaces in E³ and Eⁿ, Ann. of Math., 80 (1964), 340-364.
10) R. Osserman, A survey of minimal surfaces, Van Nostrand, New York, 1969.
11) F. Xavier, The Gauss map of a complete non-flat minimal surface cannot omit 7 points of the sphere, Ann. of Math., 113 (1981), 211-214.

Right : [1] L. A. Ahlfors, Conformal invariants, Topics in geometric function theory, McGraw-Hill, New York, 1973.
[2] C. C. Chen, On the image of the generalized Gauss map of a complete minimal surface in R⁴, Pacific J. Math., 102 (1982), 9-14.
[3] S. S. Chern and R. Osserman, Complete minimal surfaces in euclidean n-space, J. Analyse Math., 19 (1967), 15-34.
[4] H. Fujimoto, On the Gauss map of a complete minimal surface in R^m, J. Math. Soc. Japan, 35 (1983), 279-288.
[5] H. Fujimoto, Value distribution of the Gauss maps of complete minimal surfaces in R^m, J. Math. Soc. Japan, 35 (1983), 663-681.
[6] H. Fujimoto, Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into P^N₁(C)×…×P^N_k(C), Japanese J. Math., 11(1985), 233-264.
[7] R. Narasimhan, Complex analysis in one variable, Birkhäuser, Boston, 1985.
[8] R. Osserman, Minimal surfaces in the large, Comment. Math. Helv., 35 (1961), 65-76.
[9] R. Osserman, Global properties of minimal surfaces in E³ and Eⁿ, Ann. of Math., 80 (1964), 340-364.
[10] R. Osserman, A survey of minimal surfaces, Van Nostrand, New York, 1969.
[11] F. Xavier, The Gauss map of a complete non-flat minimal surface cannot omit 7 points of the sphere, Ann. of Math., 113 (1981), 211-214.

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

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