On the Gauss curvature of minimal surfaces

Hirotaka FUJIMOTO

doi:10.2969/jmsj/04430427

Hirotaka FUJIMOTO

著者情報

ジャーナルフリー

1992 年 44 巻 3 号 p. 427-439

DOI https://doi.org/10.2969/jmsj/04430427

詳細

Published: 1992 Received: 1991/07/19 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: 引用文献情報訂正内容: Wrong : 1) L. V. Ahlfors, An extension of Schwarz's lemma, Trans. Amer. Math. Soc., 43 (1938), 359-364.
2) L. V. Ahlfors, Conformal invariants, Topics in Geometric Function Theory, McGraw Hill, New York, 1973.
3) S. Bernstein, Über ein geometriches Theorem and seine Anwendung auf die par-tiellen Differentialgleichungen vom elliptischen Typus, Math. Z., 26 (1927), 551-558.
4) H. Fujimoto, On the number of exceptional values of the Gauss map of minimal surfaces, J. Math. Soc. Japan, 40 (1988), 235-247.
5) H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, J. Differential Geom., 29 (1989), 245-262.
6) H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, II, J. Differential Geom., 31 (1990), 365-385.
7) H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, III, Nagoya Math. J., 124 (1991), 13-40.
8) E. Heinz, Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen, (1952), 51-56.
9) X. Mo and R. Osserman, On the Gauss map and total curvature of complete minimal surfaces and an extension of Fujimoto's theorem, J. Differential Geom., 31 (1990), 343-355.
10) R. Osserman, An analogue of the Heinz-Hopf inequality, J. Math. Mech., 8 (1959), 383-385.
11) R. Osserman, On the Gauss curvature of minimal surfaces, Trans. Amer. Math. Soc., 96 (1960), 115-128.
12) R. Osserman, Global properties of minimal surfaces in E³ and Eⁿ, Ann. of Math., 80 (1964), 340-364.
13) R. Osserman, A survey of minimal surfaces, 2nd edition, Dover Publ. Inc., New York, 1986.
14) A. Ros, The Gauss map of minimal surfaces, preprint.

Right : [1] L. V. Ahlfors, An extension of Schwarz's lemma, Trans. Amer. Math. Soc., 43 (1938), 359-364.
[2] L. V. Ahlfors, Conformal invariants, Topics in Geometric Function Theory, McGraw Hill, New York, 1973.
[3] S. Bernstein, Über ein geometriches Theorem and seine Anwendung auf die par-tiellen Differentialgleichungen vom elliptischen Typus, Math. Z., 26 (1927), 551-558.
[4] H. Fujimoto, On the number of exceptional values of the Gauss map of minimal surfaces, J. Math. Soc. Japan, 40 (1988), 235-247.
[5] H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, J. Differential Geom., 29 (1989), 245-262.
[6] H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, II, J. Differential Geom., 31 (1990), 365-385.
[7] H. Fujimoto, Modified defect relations for the Gauss map of minimal surfaces, III, Nagoya Math. J., 124 (1991), 13-40.
[8] E. Heinz, Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen, (1952), 51-56.
[9] X. Mo and R. Osserman, On the Gauss map and total curvature of complete minimal surfaces and an extension of Fujimoto's theorem, J. Differential Geom., 31 (1990), 343-355.
[10] R. Osserman, An analogue of the Heinz-Hopf inequality, J. Math. Mech., 8 (1959), 383-385.
[11] R. Osserman, On the Gauss curvature of minimal surfaces, Trans. Amer. Math. Soc., 96 (1960), 115-128.
[12] R. Osserman, Global properties of minimal surfaces in E³ and Eⁿ, Ann. of Math., 80 (1964), 340-364.
[13] R. Osserman, A survey of minimal surfaces, 2nd edition, Dover Publ. Inc., New York, 1986.
[14] A. Ros, The Gauss map of minimal surfaces, preprint.

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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