螺旋面在中曲率流场中的旋转/平移
Helicoidal surfaces rotating/translating under the mean curvature flow
摘要：
描述了欧几里得空间中浸没超曲面在中曲率流下的所有可能的自相似运动，并导出了相应的超曲面方程。然后，我们提出了一个新的双参数家庭沉浸螺旋面的旋转/下恒速平移流。我们看看他们的限制行为的螺距的螺旋运动到0，并比较它与经典的螺旋极小曲面的限制行为。最后，我们给出了常中曲率螺旋曲面族中浸没圆柱的分类。
英文摘要：
We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
