论文标题
horo-convex Hypersurfaces具有$ \ mathbb {h}^{n+1} $的规定移动的高斯曲面
Horo-convex hypersurfaces with prescribed shifted Gauss curvatures in $\mathbb{H}^{n+1}$
论文作者
论文摘要
在本文中，我们考虑了$ \ mathbb {h}^{n+1} $中的horo-convex Hyperfaces的规定的高斯曲率方程。在某种足够的条件下，我们根据方程解决方案的先验估计值获得了标准学位理论的存在。与空间形式中规定的Weingarten曲率问题不同，我们不会对方程右侧函数的径向导数施加符号条件，以证明由于$ \ MathBb {H}^{N+1} $的Hypersurfaces的存在而存在。
In this paper, we consider prescribed shifted Gauss curvature equations for horo-convex hypersurfaces in $\mathbb{H}^{n+1}$. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the equations. Different from the prescribed Weingarten curvature problem in space forms, we do not impose a sign condition for radial derivative of the functions in the right-hand side of the equations to prove the existence due to the horo-covexity of hypersurfaces in $\mathbb{H}^{n+1}$.
