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Article overview
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Helicoidal minimal surfaces of prescribed genus | David Hoffman
; Martin Traizet
; Brian White
; | Date: |
1 Aug 2015 | Abstract: | For 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 | Services: | Forum | Review | PDF | Favorites |
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