Helicoidal surfaces with constant anisotropic mean curvature

Abstract

We study surfaces which are in equilibrium for an anisotropic surface energy and which are invariant under a helicoidal motion. For anisotropic functionals with axially symmetric Wulff shapes, we generalize the recently developed twizzler representation [Perdomo, O., A dynamical interpretation of the profile curve of CMC twizzlers surfaces, e-print arXiv:1001.5198v1] to the anisotropic case and show how all helicoidal constant anisotropic mean curvature surfaces can be obtained by quadratures. When the functional is not axially symmetric, we produce a canonical critical point which is analogous to the classical helicoid.