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Transactions of the American Mathematical Society

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

 

 

A Picard theorem with an application to minimal surfaces. II


Author: Peter Hall
Journal: Trans. Amer. Math. Soc. 325 (1991), 895-902
MSC: Primary 53A10; Secondary 32H25
DOI: https://doi.org/10.1090/S0002-9947-1991-1013332-2
MathSciNet review: 1013332
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Abstract: Let $ f:{\mathbf{C}} \to {{\mathbf{R}}^n}$ be a parabolic minimal surface such that the normals to $ f$ omit $ n + k$ directions in general position, $ k \geq 0$. We obtain sharp bounds on the dimension of the affine span of $ f$ and of the linear span of the Gauss map of $ f$.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1013332-2
Article copyright: © Copyright 1991 American Mathematical Society