Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems
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- 作者：Yong Huang ; Erwin Lutwak ; Deane Yang ; Gaoyong Zhang
- 关键词：2010 Math. Subj. Classification52A38 ; 35J20
- 刊名：Acta Mathematica
- 出版年：2016
- 出版时间：June 2016
- 年：2016
- 卷：216
- 期：2
- 页码：325-388
- 全文大小：781 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer Netherlands
- ISSN：1871-2509
- 卷排序：216
文摘
A longstanding question in the dual Brunn–Minkowski theory is “What are the dual analogues of Federer’s curvature measures for convex bodies?” The answer to this is provided. This leads naturally to dual versions of Minkowski-type problems: What are necessary and sufficient conditions for a Borel measure to be a dual curvature measure of a convex body? Sufficient conditions, involving measure concentration, are established for the existence of solutions to these problems.