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arXiv · 1106.4583

Helicoidal surfaces rotating/translating under the mean curvature flow

Hoeskuldur P. Halldorsson
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Abstract

We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces.

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Hoeskuldur P. Halldorsson. 2011-06-22. Helicoidal surfaces rotating/translating under the mean curvature flow. https://doi.org/10.1007/s10711-012-9716-2

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