Translators of the Gauss curvature flow

2022/01/14 by Aydin, Muhittin Evren, López, Rafael
#35J96 #53A15 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.05347

Abstract

A K^α-translator is a surface in Euclidean space \r³ 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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