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arXiv · 1110.1068

A conservation approach to helicoidal surfaces of constant mean curvature in R^3, S^3 and H^3

Nick Edelen
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Abstract

We develop a conservation law for constant mean curvature (CMC) surfaces introduced by Korevaar, Kusner and Solomon, and provide a converse, so as to characterize CMC surfaces by a conservation law. We work with `twizzler' construction, which applies a screw-motion to some base curve. We show that, excluding cylinders, CMC helicoidal surfaces can be completely determined by a first-order ODE of the base curve. Further, we demonstrate that in R^3 this condition is equivalent to the treadmillsled characterization of helicoidal CMC surfaces given by O. Perdomo.

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Nick Edelen. 2011-10-05. A conservation approach to helicoidal surfaces of constant mean curvature in R^3, S^3 and H^3. https://arxiv.org/abs/1110.1068

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