负指标的对偶Minkowski问题
The dual Minkowski problem for negative indices
摘要：
最近，黄，Lutwak，Yang和Zhang发现了Federer曲率测度的双曲率测度（称为双曲率测度）（ACTA，2016）。在同一篇论文中，他们提出了对偶Minkowski问题，对偶曲率测度的特征问题，并证明了当指标q在（0，n）中时存在结果。对偶Minkowski问题包括Aleksandrov问题（q = 0）和对数Minkowski问题（q = n）作为特殊情况。在目前的工作中，对偶Minkowski问题的一个完整的解决方案，当q < 0，包括存在性和唯一性，提出。
英文摘要：
Recently, the duals of Federer's curvature measures, called dual curvature measures, were discovered by Huang, Lutwak, Yang, and Zhang (ACTA, 2016). In the same paper, they posed the dual Minkowski problem, the characterization problem for dual curvature measures, and proved existence results when the index, q, is in (0,n). The dual Minkowski problem includes the Aleksandrov problem (q = 0) and the logarithmic Minkowski problem (q = n) as special cases. In the current work, a complete solution to the dual Minkowski problem whenever q < 0, including both existence and uniqueness, is presented.
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