Value distribution of the Gauss maps of complete minimal surfaces in Rm

Hirotaka FUJIMOTO

doi:10.2969/jmsj/03540663

Value distribution of the Gauss maps of complete minimal surfaces in R^m

Hirotaka FUJIMOTO

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1983 Volume 35 Issue 4 Pages 663-681

DOI https://doi.org/10.2969/jmsj/03540663

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Published: 1983 Received: September 13, 1982 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 M. Ozawa on the occasion of his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica, 7 (1933), 5-31.
2) S. S. Chern and R. Osserman, Complete minimal surfaces in euclidean n-space, J. Analyse Math., 19 (1967), 15-34.
3) H. Fujimoto, The defect relations for the derived curves of a holomorphic curve in Pⁿ (C), Tohoku Math. J., 34 (1982), 141-160.
4) H. Fujimoto, On the Gauss map of a complete minimal surface in R^m, J. Math. Soc. Japan, 35 (1983), 279-288.
5) W. K. Hayman, Meromorphic functions, Oxford Mathematical Monograph, Clarendon Press, Oxford, 1964.
6) W. K. Hayman and P. B. Kennedy, Subharmonic functions, Academic Press, London, 1976.
7) D. A. Hoffman and R. Osserman, The geometry of the generalized Gauss map, Amer. Math. Soc. Memoir, 236, 1980.
8) H. B. Lawson, Lectures on minimal submanifolds, Vol. 1, Publish or Perish Inc., Berkeley, 1980.
9) R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929.
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, Van Nostrand Reinhold, New York, 1969.
12) R. Osserman, Minimal surfaces, Gauss maps, total curvature, eigenvalue estimates, and stability, The Chern Symposium 1979, Springer-Verlag.
13) 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.
14) 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] H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica, 7 (1933), 5-31.
[2] S. S. Chern and R. Osserman, Complete minimal surfaces in euclidean n-space, J. Analyse Math., 19 (1967), 15-34.
[3] H. Fujimoto, The defect relations for the derived curves of a holomorphic curve in Pⁿ (C), Tôhoku Math. J., 34 (1982), 141-160.
[4] H. Fujimoto, On the Gauss map of a complete minimal surface in R^m, J. Math. Soc. Japan, 35 (1983), 279-288.
[5] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monograph, Clarendon Press, Oxford, 1964.
[6] W. K. Hayman and P. B. Kennedy, Subharmonic functions, Academic Press, London, 1976.
[7] D. A. Hoffman and R. Osserman, The geometry of the generalized Gauss map, Amer. Math. Soc. Memoir, 236, 1980.
[8] H. B. Lawson, Lectures on minimal submanifolds, Vol. 1, Publish or Perish Inc., Berkeley, 1980.
[9] R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929.
[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, Van Nostrand Reinhold, New York, 1969.
[12] R. Osserman, Minimal surfaces, Gauss maps, total curvature, eigenvalue estimates, and stability, The Chern Symposium 1979, Springer-Verlag.
[13] 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.
[14] S. T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J., 25 (1976), 659-670.

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

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