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<p>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 where 0 &lt; <i>q</i> ⩽ 4. An improved nonuniqueness result when <i>q</i> &gt; 4 is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the <i>L</i><sub><i>p</i></sub>-Alexandrov problem is obtained for <i>p</i> &lt; 0.</p>

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On the number of solutions to the planar dual Minkowski problem

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Yannan Liu,
  • Jian Lu

摘要

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 where 0 < q ⩽ 4. An improved nonuniqueness result when q > 4 is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the Lp-Alexandrov problem is obtained for p < 0.