论文标题
高斯曲率流的翻译器
Translators of the Gauss curvature flow
论文作者
论文摘要
a $ k^α$ - 翻译器是欧几里得空间中的表面$ \ r^3 $，它通过沿空间方向进行翻译而移动，在$ k^α$ - 流下，其中$ k $是高斯曲率，而$α$是一个常数。我们对旋转对称的所有$ k^α$ translators进行了分类。特别是，我们证明，对于每个$α$，都有一个$ k^α$ translator将旋转轴正交相交。我们还描述了一个螺旋运动的一组螺旋运动组和通过变量分离获得的翻译器的所有$ k^α$ thranslators不变。
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.
