General \(L_{p}\) -dual Blaschke bodies and the applications
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- 作者：Jianye Wang ; Weidong Wang
- 关键词：general \(L_{p}\) ; dual Blaschke body ; extremal value ; \(L_{p}\) ; Busemann ; Petty problem
- 刊名：Journal of Inequalities and Applications
- 出版年：2015
- 出版时间：December 2015
- 年：2015
- 卷：2015
- 期：1
- 全文大小：1,430 KB
- 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
- 出版者：Springer International Publishing
- ISSN：1029-242X
文摘
Lutwak defined the dual Blaschke combination of star bodies. In this paper, based on the \(L_{p}\)-dual Blaschke combination of star bodies, we define the general \(L_{p}\)-dual Blaschke bodies and obtain the extremal values of their volume and \(L_{p}\)-dual affine surface area. Further, as the applications, we study two negative forms of the \(L_{p}\)-Busemann-Petty problems.