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arxiv: 1509.00786 · v1 · pith:UMEWXKWPnew · submitted 2015-09-02 · 🧮 math.AP

Solution of the fractional Allen-Cahn equation which are invariant under screw motion

Eleonora Cinti , Juan Davila , Manuel del Pino This is my paper
classification 🧮 math.AP
keywords allen-cahnequationfractionalhelicoidsinvariantunderadditioncurvature
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We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in $\mathbb R^3$, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature.

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