关于平面对偶 Minkowski 问题解的个数
偏微分方程分析
2024-07-30 v2 微分几何
摘要
本文研究二维平面中的对偶 Minkowski 问题。通过结合带参数积分的理论分析与数值估计，我们找到了在常数对偶曲率情形且 时该问题解的个数。同时得到了当 时改进的非唯一性结果。作为一个应用，获得了 -Alexandrov 问题在 时解的唯一性与非唯一性结果。
引用
@article{arxiv.2209.15385,
title = {On the number of solutions to the planar dual Minkowski problem},
author = {YanNan Liu and Jian Lu},
journal= {arXiv preprint arXiv:2209.15385},
year = {2024}
}
备注
The first time we submitted this paper for publication is June 4, 2022. We noticed the paper H. Li & Y. Wan [29] submitted to arXiv on September 29, 2022. The method and result in our Section 3 are also obtained in [29]. Due to non-monotonicity, the paper [29] does not solve the uniqueness problem for 3<q<=4. While our paper has solved it by numerical estimation in Section 4