Translators of the Gauss curvature flow

A $K^α$-translator is a surface in Euclidean space $\r^3$ that moves by translations in a spatial direction and under the $K^α$-flow, where $K$ is the Gauss curvature and $α$ is a constant. We classify all $K^α$-translators that are rotationally symmetric. In particular, we prove that for each $α$ there is a $K^α$-translator intersecting orthogonally the rotation axis. We also describe all $K^α$-translators invariant by a uniparametric group of helicoidal motions and the translators obtained by separation of variables.

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