Values of Gauss maps of complete minimal surfaces in ℝ^{𝕞} on annular ends

Jin, Lu; Ru, Min

doi:10.1090/S0002-9947-06-04126-2

Values of Gauss maps of complete minimal surfaces in ${\mathbb {R}}^{m}$ on annular ends
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Trans. Amer. Math. Soc. 359 (2007), 1547-1553 Request permission

Abstract:

Let $M$ be a complete minimal surface in ${\mathbb {R}}^{m}$ and let $A$ be an annular end of $M$ which is conformal to $\{z~|~ 0 < 1/r<|z|<r\}$, where $z$ is the conformal coordinate. Let $G$ be the generalized Gauss map of $M$. We show that $G(A)$ must intersect every hyperplane in ${\mathbb {P}}^{m-1}({\mathbb {C}})$, with the possible exception of $m(m+1)/2$ hyperplanes in general position.

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