scholarly journals The Arch Of Projection - Body and Mind in Herzog & de Meuron’s Architecture

2011 ◽  
Vol 42 (2) ◽  
pp. 19-26
Author(s):  
Mariann Simon
Keyword(s):  
Projection Body

scholarly journals Inequalities for the Surface Area of Projections of Convex Bodies

2018 ◽  
Vol 70 (4) ◽  
pp. 804-823 ◽  
Author(s):  
Apostolos Giannopoulos ◽  
Alexander Koldobsky ◽  
Petros Valettas
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Convex Bodies ◽  
Maximal Surface ◽  
Projection Body ◽  
Projections Of Convex Bodies ◽  
Lower Dimensional

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.

scholarly journals The Arch Of Projection - Body and Mind in Herzog & de Meuron’s Architecture

2014 ◽  
Vol 42 (2) ◽  
pp. 19-26
Author(s):  
Mariann Simon
Keyword(s):  
Projection Body

scholarly journals Iterations of the projection body operator and a remark on Petty's conjectured projection inequality

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

Inequalities of the quermassintegrals for the Lp-projection body and the Lp-centroid body

2010 ◽  
Vol 30 (1) ◽  
pp. 359-368 ◽  
Author(s):  
Wang Weidong ◽  
Leng Gangsong
Keyword(s):  
Projection Body ◽  
Lp Projection Body

scholarly journals On Projection Bodies of Order One

2009 ◽  
Vol 52 (3) ◽  
pp. 349-360 ◽  
Author(s):  
Stefano Campi ◽  
Paolo Gronchi
Keyword(s):  
Convex Body ◽  
Support Function ◽  
The Body ◽  
Existence Problem ◽  
Orthogonal Projections ◽  
Projection Body ◽  
Strictly Convex ◽  
Mean Width ◽  
Dimension One ◽  
Projection Bodies

AbstractThe projection body of order one Π1K of a convex body K in ℝn is the body whose support function is, up to a constant, the average mean width of the orthogonal projections of K onto hyperplanes through the origin.The paper contains an inequality for the support function of Π1K, which implies in particular that such a function is strictly convex, unless K has dimension one or two. Furthermore, an existence problem related to the reconstruction of a convex body is discussed to highlight the different behavior of the area measures of order one and of order n – 1.

scholarly journals VOLUME INEQUALITIES FOR Lp-JOHN ELLIPSOIDS AND THEIR DUALS

2007 ◽  
Vol 49 (3) ◽  
pp. 469-477
Author(s):  
LU FENGHONG ◽  
LENG GANGSONG
Keyword(s):  
Projection Body ◽  
Polar Projection ◽  
Strengthened Version ◽  
John Ellipsoid

AbstractIn this paper, we establish some inequalities among the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual, which are the strengthened version of known results. We also prove inequalities among the polar of the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual.

CHORD POWER INTEGRALS OF SIMPLICES

2009 ◽  
Vol 02 (04) ◽  
pp. 557-565
Author(s):  
Wing-Sum Cheung ◽  
Ge Xiong
Keyword(s):  
Type Inequality ◽  
Projection Body ◽  
Polar Projection ◽  
Difference Body ◽  
Dual Quermassintegrals

In this paper, we obtain a formula relating the chord power integrals of a simplex K and the dual quermassintegrals of its difference body DK. As interesting applications, we express the volumes of difference body DK and polar projection body Π*K in terms of the volume of simplex K. Santaló-type inequality for chord power integrals of simplex is also established.

scholarly journals A type of monotonicity on the L_p centroid body and L_p projection body

2005 ◽  
pp. 735-742
Author(s):  
Wei-Dong Wang ◽  
Lu Fenghong ◽  
Leng Gangsong
Keyword(s):  
Projection Body

scholarly journals Lp−Winterniz problem on firey projection of convex bodies

2014 ◽  
Vol 45 (2) ◽  
pp. 179-193
Author(s):  
Tong Yi MA ◽  
Li Li Zhang
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Convex Bodies ◽  
Affine Surface ◽  
Projection Body ◽  
Affine Surface Area ◽  
Funk Transform

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.

The Orlicz Brunn–Minkowski Inequality for the Projection Body

2019 ◽  
Vol 30 (2) ◽  
pp. 2253-2272 ◽  
Author(s):  
Du Zou ◽  
Ge Xiong
Keyword(s):  
Minkowski Inequality ◽  
Projection Body
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