Hypersurfaces with Li-normalization and Prescribed Gauss–Kronecker Curvature
Hypersurfaces with Li-normalization and Prescribed Gauss–Kronecker Curvature
复制标题
DOI：
10.1007/s00025-011-0106-0
复制
发表时间：
2011-04
影响因子：
2.2
通讯作者：
Yadong Wu;Guosong Zhao
中科院分区：
文献类型：
--
作者：
Yadong Wu;Guosong Zhao
考虑到凸函数图的Li正规化，我们得到了具有给定的Gauss-Kronecker曲率的超曲面的偏微分方程组。我们用Dirichlet边界条件解了两个关联的Monge-Ampère方程，从而构造了双曲Li超曲面，使得它们的Gauss-Kronecker曲率是预定的函数。
Considering the Li-normalization of the graph of a convex function, we derive the PDEs of hypersurfaces with prescribed Gauss–Kronecker curvature. We solve two linked Monge–Ampère equations with Dirichlet boundary conditions and thus construct hyperbolic Li hypersurfaces such that their Gauss–Kronecker curvatures are the prescribed functions.