Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A Picard theorem with an application to minimal surfaces

Author: Peter Hall
Journal: Trans. Amer. Math. Soc. 314 (1989), 597-603
MSC: Primary 53A10; Secondary 32H25
MathSciNet review: 978376
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a Picard theorem for holomorphic maps from $ {\mathbf{C}}$ to a quadric hypersurface. This implies a theorem on the number of directions in general position omitted by the normals to a minimal surface of the conformal type of $ {\mathbf{C}}$.

References [Enhancements On Off] (What's this?)

  • [1] S.-S. Chern and R. Osserman, Complete minimal surfaces in Euclidean $ n$-space, J. Analyse Math. 19 (1967), 15-34. MR 0226514 (37:2103)
  • [2] O. Forster, Lectures on Riemann surfaces, Springer, New York, 1981. MR 648106 (83d:30046)
  • [3] M. L. Green, Holomorphic maps into complex projective space omitting hyperplanes, Trans. Amer. Math. Soc. 169 (1972), 89-103. MR 0308433 (46:7547)
  • [4] -, Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math. 97 (1975), 43-75. MR 0367302 (51:3544)
  • [5] D. A. Hoffman and R. Osserman, The geometry of the generalized Gauss map, Mem. Amer. Math. Soc., vol. 28, no. 236, 1980. MR 587748 (82b:53012)
  • [6] S. Lang, Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc. (N.S.) 14 (1986), 159-205. MR 828820 (87h:32051)
  • [7] H. B. Lawson, Jr., Lectures on minimal submanifolds, vol. I, Publish or Perish, Berkeley, Calif., 1980. MR 576752 (82d:53035b)
  • [8] R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929; Chelsea, New York, reprinted 1974. MR 0417418 (54:5468)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53A10, 32H25

Retrieve articles in all journals with MSC: 53A10, 32H25

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society