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Article Dans Une Revue Acta Mathematica Année : 2016

HELICOIDAL MINIMAL SURFACES OF PRESCRIBED GENUS

Résumé

For every genus g, we prove that S^2 × 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.
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Dates et versions

hal-01270167 , version 1 (05-02-2016)

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David Hoffman, Martin Traizet, Brian White. HELICOIDAL MINIMAL SURFACES OF PRESCRIBED GENUS. Acta Mathematica, 2016, 216 (2), pp.217--323. ⟨hal-01270167⟩
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