projection body
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2020 ◽  
pp. 1-14
Author(s):  
Zhongwen Tang ◽  
Lin Si


2019 ◽  
Vol 30 (2) ◽  
pp. 2253-2272 ◽  
Author(s):  
Du Zou ◽  
Ge Xiong


2018 ◽  
Vol 340 ◽  
pp. 914-959 ◽  
Author(s):  
Niufa Fang ◽  
Jiazu Zhou


2018 ◽  
Vol 70 (4) ◽  
pp. 804-823 ◽  
Author(s):  
Apostolos Giannopoulos ◽  
Alexander Koldobsky ◽  
Petros Valettas

AbstractWe provide general inequalities that compare the surface area S(K) of a convex body K in ℝn to the minimal, average, or maximal surface area of its hyperplane or lower dimensional projections. We discuss the same questions for all the quermassintegrals of K. We examine separately the dependence of the constants on the dimension in the case where K is in some of the classical positions or K is a projection body. Our results are in the spirit of the hyperplane problem, with sections replaced by projections and volume by surface area.



2017 ◽  
Vol 272 (2) ◽  
pp. 613-630 ◽  
Author(s):  
C. Saroglou ◽  
A. Zvavitch
Keyword(s):  




2014 ◽  
Vol 45 (2) ◽  
pp. 179-193
Author(s):  
Tong Yi MA ◽  
Li Li Zhang

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.





2011 ◽  
pp. 181-192
Author(s):  
Tong-Yi Ma ◽  
Wei-Dong Wang




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