We study the motion of a hypersurface in a cylinder driven by its (generalized) Gauss curvature. Some special cases of the problem can be used to model the abrasion of a stick on its ends. First we consider the case where the slope of the hypersurface on the cylinder boundary is a positive constant $h$, and seek for a radially symmetric translating solution. Then we consider the case where the boundary slope of the hypersurface is equal to $h\left(u\right)$, with $u$ representing the hypersurface function and $h$ being a positive function satisfying $h\left(u\right)\to h^{\pm }>0$ as $u\to \pm \infty$. We construct the unique entire solution to this problem and show that it connects a translating solution with boundary slope $h^{-}$ at $t=-\infty$ and another translating solution with boundary slope $h^{+}$ at $t=+\infty$.

我们研究了由（广义）高斯曲率驱动的圆柱体中超曲面的运动。问题的一些特殊情况可以用来模拟棍子两端的磨损。首先，我们考虑圆柱面边界上的超曲面的坡度为正常数的情况$H$，并寻求径向对称的平移解决方案。然后我们考虑超曲面的边界斜率等于$H（ü）$，带有 $ü$ 代表超曲面函数和 $H$ 是令人满意的积极功能 $H（ü）\to H^{\pm }>0$ 如 $ü\to \pm \infty$。我们构造了这个问题的唯一整体解，并表明它将平移解与边界斜率连接起来$H^{-}$ 在 $Ť=-\infty$ 和另一个具有边界斜率的平移解 $H^{+}$ 在 $Ť=+\infty$。