Article

# Helicoidal surfaces rotating/translating under the mean curvature flow

Geometriae Dedicata (Impact Factor: 0.47). 06/2011; DOI: 10.1007/s10711-012-9716-2
Source: arXiv

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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