标题： 欧几里得空间中高斯曲率流的孤立子刚性 显示英文标题

标题： Rigidity of solitons of the Gauss curvature flow in Euclidean space

摘要： 在本文中，我们考虑欧几里得空间中高斯曲率流的$\lambda$-平移孤立子和$\lambda$-缩小时解。 我们证明平面和圆柱面是具有常平均曲率的$\lambda$-平移孤立子。 我们还证明平面、球面和圆柱面是具有常平均曲率的$\lambda$-缩小时解。 我们给出了具有一个常主曲率的$\lambda$-平移孤立子和$\lambda$-缩小时解的分类。 显示英文摘要

摘要： In this paper, we consider $\lambda$-translating solitons and $\lambda$-shrinkers of the Gauss curvature flow in Euclidean space. We prove that planes and circular cylinders are the only $\lambda$-translating solitons with constant mean curvature. We also prove that planes, spheres and circular cylinders are the only $\lambda$-shrinkers with constant mean curvature. We give a classification of the $\lambda$-translating solitons and $\lambda$-shrinkers with one constant principal curvature.