The dual Minkowski problem for negative indices

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• 作者：Yiming Zhao
• 关键词：Mathematics Subject Classification52A40
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：56
• 期：2
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0835
• 卷排序：56

文摘

Recently, the duals of Federer’s curvature measures, called dual curvature measures, were discovered by Huang et al. (Acta Math 216:325–388, 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.