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arXiv · 2209.15385

On the number of solutions to the planar dual Minkowski problem

YanNan Liu·Jian Lu
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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 $0 4$ is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the $L_p$-Alexandrov problem is obtained for $p<0$.

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YanNan Liu, Jian Lu. 2022-09-30. On the number of solutions to the planar dual Minkowski problem. https://arxiv.org/abs/2209.15385

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