scholarly journals Modified Shephard’s problem on projections of convex bodies

2008 ◽  
Vol 168 (1) ◽  
pp. 221-238 ◽  
Author(s):  
Vladyslav Yaskin
Keyword(s):  
Convex Bodies ◽  
Projections Of Convex Bodies

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.

Low dimensional sections versus projections of convex bodies

2006 ◽  
Vol 153 (1) ◽  
pp. 45-60 ◽  
Author(s):  
Piotr Mankiewicz ◽  
Nicole Tomczak-Jaegermann
Keyword(s):  
Convex Bodies ◽  
Low Dimensional ◽  
Projections Of Convex Bodies

scholarly journals Almost ellipsoidal sections and projections of convex bodies

1975 ◽  
Vol 77 (3) ◽  
pp. 529-546 ◽  
Author(s):  
D. G. Larman ◽  
P. Mani
Keyword(s):  
Convex Body ◽  
High Dimension ◽  
Interior Point ◽  
Convex Bodies ◽  
Symmetric Convex Body ◽  
Symmetric Convex ◽  
Centrally Symmetric ◽  
Dimensional Section ◽  
Projections Of Convex Bodies

In (1) Dvoretsky proved, using very ingenious methods, that every centrally symmetric convex body of sufficiently high dimension contains a central k-dimensional section which is almost spherical. Here we shall extend this result (Corollary to Theorem 2) to k-dimensional sections through an arbitrary interior point of any convex body.

scholarly journals Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies

2018 ◽  
Vol 18 (3) ◽  
pp. 345-354 ◽  
Author(s):  
Silouanos Brazitikos ◽  
Apostolos Giannopoulos ◽  
Dimitris-Marios Liakopoulos
Keyword(s):  
Convex Bodies ◽  
Upper Bounds ◽  
Compact Set ◽  
Uniform Cover ◽  
Cover Inequalities ◽  
Projections Of Convex Bodies ◽  
Lower Dimensional

AbstractThe classical Loomis–Whitney inequality and the uniform cover inequality of Bollobás and Thomason provide upper bounds for the volume of a compact set in terms of its lower dimensional coordinate projections. We provide further extensions of these inequalities in the setting of convex bodies. We also establish the corresponding dual inequalities for coordinate sections; these uniform cover inequalities for sections may be viewed as extensions of Meyer’s dual Loomis–Whitney inequality.

scholarly journals Distribution functions of sections and projections of convex bodies

2016 ◽  
Vol 95 (1) ◽  
pp. 52-72 ◽  
Author(s):  
Jaegil Kim ◽  
Vladyslav Yaskin ◽  
Artem Zvavitch
Keyword(s):  
Convex Bodies ◽  
Distribution Functions ◽  
Projections Of Convex Bodies

Projections of convex bodies and the fourier transform

2004 ◽  
Vol 139 (1) ◽  
pp. 361-380 ◽  
Author(s):  
Alexander Koldobsky ◽  
Dmitry Ryabogin ◽  
Artem Zvavitch
Keyword(s):  
Fourier Transform ◽  
Convex Bodies ◽  
The Fourier Transform ◽  
Projections Of Convex Bodies

scholarly journals The concept of duality for measure projections of convex bodies

2008 ◽  
Vol 254 (10) ◽  
pp. 2648-2666 ◽  
Author(s):  
Shiri Artstein-Avidan ◽  
Vitali Milman
Keyword(s):  
Convex Bodies ◽  
Projections Of Convex Bodies
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