论文标题
关于平面双minkowski问题的解决方案数量
On the number of solutions to the planar dual Minkowski problem
论文作者
论文摘要
在本文中研究了二维平面中的双重Minkowski问题。通过将积分与参数的理论分析和数值估计结合在一起，我们在$ 0 <q \ leq4 $时找到了恒定双曲率情况的解决方案的数量。当还获得$ Q> 4 $时，将会得到改进的非专业结果。作为一个应用程序，对于$ p <0 $，获得了$ l_p $ -alexandrov问题的独特性和唯一性解决方案的结果。
The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the constant dual curvature case when $0<q\leq4$. An improved nonuniqueness result when $q>4$ is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the $L_p$-Alexandrov problem is obtained for $p<0$.
