On the number of solutions to the planar dual Minkowski problem
Abstract
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 . An improved nonuniqueness result when is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the -Alexandrov problem is obtained for .
Keywords
Cite
@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}
}
Comments
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