On the Gauss map of a complete minimal surface in Rm

Hirotaka FUJIMOTO

doi:10.2969/jmsj/03520279

On the Gauss map of a complete minimal surface in R^m

Hirotaka FUJIMOTO

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ジャーナルフリー

1983 年 35 巻 2 号 p. 279-288

DOI https://doi.org/10.2969/jmsj/03520279

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Published: 1983 Received: 1982/01/11 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : On the Gauss map of a complete minimal surface in R_m
Right : On the Gauss map of a complete minimal surface in R^m

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) E. Borel, Sur les zéros des fonctions entières, Acta Math., 20 (1897), 357-396.
2) H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica, 7 (1933), 5-31.
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 families of meromorphic maps into the complex projective space, Nagoya Math. J., 54 (1974), 21-51.
5) H. Fujimoto, The defect relations for the derived curves of a holomorphic curve in P_n(C), Tohoku Math. J., 34 (1982), 141-160.
6) W.K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, 1964.
7) H.B. Lawson, Lectures on minimal submanifolds, Vol. 1, Publish or Perish Inc., Berkeley, 1980.
8) R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929.
9) R. Osserman, Minimal surfaces in the large, Comment, Math. Helv., 35 (1961), 65-76.
10) R. Osserman, A survey of minimal surfaces, Van Nostrand Reinhold, New York, 1969.
11) J. Suzuki and N. Toda, Some notes on the theory of holomorphic curves, Nagoya Math. J., 81 (1981), 79-89.
12) H. Weyl and J. Weyl, Meromorphic functions and analytic curves, Princeton Univ. Press, Princeton, New Jersey, 1943.
13) H. Wu, The equidistribution theory of holomorphic curves, Princeton Univ. Press, Princeton, New Jersey, 1970.
14) 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.
15) S.T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J., 25 (1976), 659-670.

Right : [1] E. Borel, Sur les zéros des fonctions entières, Acta Math., 20 (1897), 357-396.
[2] H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica, 7 (1933), 5-31.
[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 families of meromorphic maps into the complex projective space, Nagoya Math. J., 54 (1974), 21-51.
[5] H. Fujimoto, The defect relations for the derived curves of a holomorphic curve in P_n(C), Tôhoku Math. J., 34 (1982), 141-160.
[6] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, 1964.
[7] H. B. Lawson, Lectures on minimal submanifolds, Vol. 1, Publish or Perish Inc., Berkeley, 1980.
[8] R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929.
[9] R. Osserman, Minimal surfaces in the large, Comment, Math. Helv., 35 (1961), 65-76.
[10] R. Osserman, A survey of minimal surfaces, Van Nostrand Reinhold, New York, 1969.
[11] J. Suzuki and N. Toda, Some notes on the theory of holomorphic curves, Nagoya Math. J., 81 (1981), 79-89.
[12] H. Weyl and J. Weyl, Meromorphic functions and analytic curves, Princeton Univ. Press, Princeton, New Jersey, 1943.
[13] H. Wu, The equidistribution theory of holomorphic curves, Princeton Univ. Press, Princeton, New Jersey, 1970.
[14] 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.
[15] S. T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J., 25 (1976), 659-670.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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