On helicoidal ends of minimal surfaces

Abstract : This article analyzes the behaviour of helicoidal ends of properly embedded minimal surfaces, namely properly embedded infinite total curvature minimal annuli of parabolic type, satisfying a growth condition on the curvature via the Gauss map, and a geometric transversality condition. Then we show that embeddedness forces the end to be asymptotic either to a plane, or a helicoid or a spiraling helicoid. In all three cases, the Gauss map can be described in very simple terms. Finally this local result yields a global corollary stating the rigidity of embedded minimal helicoids.
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Pascal Romon. On helicoidal ends of minimal surfaces. Annals of Global Analysis and Geometry, Springer Verlag, 1994, 12 (1), pp.341. ⟨10.1007/BF02108306⟩. ⟨hal-00860937⟩

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