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arXiv · 1508.00064

Helicoidal minimal surfaces of prescribed genus

David Hoffman·Martin Traizet·Brian White
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Abstract

For every genus $g$, we prove that $S^2 \times R$ contains complete, properly embedded, genus-$g$ minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also show that as the radius of the $S^2$ tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in $R^3$ that are helicoidal at infinity. We prove that helicoidal surfaces in $R^3$ of every prescribed genus occur as such limits of examples in $S^2\times R$.

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David Hoffman, Martin Traizet, Brian White. 2016-11-17. Helicoidal minimal surfaces of prescribed genus. https://arxiv.org/abs/1508.00064

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