Gauss map of minimal surfaces with ramification

Ru, Min

doi:10.1090/S0002-9947-1993-1191614-3

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

Gauss map of minimal surfaces with ramification

Author: Min Ru
Journal: Trans. Amer. Math. Soc. 339 (1993), 751-764
MSC: Primary 53A10
MathSciNet review: 1191614
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Abstract: We prove that for any complete minimal surface immersed in ${R^n}$ , if in $C{P^{n - 1}}$ there are hyperplanes ${H_j}$ in general position such that the Gauss map of is ramified over ${H_j}$ with multiplicity at least ${e_j}$ for each and

$\displaystyle \sum\limits_{j = 1}^q {\left({1 - \frac{{(n - 1)}} {{{e_j}}}} \right) > n(n + 1)/2}$

, then

must be flat.

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