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16 February 2025
 
  » arxiv » 1508.0064

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Helicoidal minimal surfaces of prescribed genus
David Hoffman ; Martin Traizet ; Brian White ;
Date 1 Aug 2015
AbstractFor every genus $g$, we prove that $S^2 imes R$ 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 $S^2 imes R$.
Source arXiv, 1508.0064
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