Lp−Winterniz problem on firey projection of convex bodies

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Published: Jun 30, 2014
DOI: https://doi.org/10.5556/j.tkjm.45.2014.1017
Keywords:
p-projection body Lp-affine surface area the generalized cosine transforms

Main Article Content

Tong Yi MA
Li Li Zhang

Abstract

For $p\geq 1$, Lutwak, Yang and Zhang introduced the concept of $p$-projection body, and Lutwak introduced the concept of $L_{p}-$ affine surface area of convex body. In this paper, we develop the Minkowski-Funk transform approach in the $L_{p}$-Brunn-Minkowski theory. We consider the question of whether $\Pi_{p}K\subseteq \Pi_{p}L$ implies $\Omega_{p}(K) \leq \Omega_{p}(L)$, where $\Pi_{p}K$ and $\Omega_{p}K$ denotes the $p-$projection body of convex body $K$ and the $L_{p}-$affine surface area of convex body $K$, respectively. We also formulate and solve a generalized $L_{p}-$Winterniz problem for Firey projections.

Article Details

How to Cite
MA, T. Y., & Zhang, L. L. (2014). Lp−Winterniz problem on firey projection of convex bodies. Tamkang Journal of Mathematics, 45(2), 179–193. https://doi.org/10.5556/j.tkjm.45.2014.1017
Issue
Vol. 45 No. 2 (2014)
Section
Papers
Author Biographies

Tong Yi MA

College ofMathematics and Statistics, Hexi University, Zhangye, Gansu 734000, P.R. China.

Li Li Zhang

College ofMathematics and Statistics, NorthwestNormal University, Lanzhou Gansu 730070, P.R. China

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