scholarly journals Variance asymptotics for random polytopes in smooth convex bodies

2013 ◽  
Vol 158 (1-2) ◽  
pp. 435-463 ◽  
Author(s):  
Pierre Calka ◽  
J. E. Yukich
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Random Polytopes

scholarly journals Approximation of smooth convex bodies by random polytopes

2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Julian Grote ◽  
Elisabeth Werner
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Random Polytopes

scholarly journals Random polytopes in smooth convex bodies

Mathematika ◽  
1992 ◽  
Vol 39 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Imre Bárány
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Random Polytopes

Random polytopes in smooth convex bodies: corrigendum

Mathematika ◽  
2004 ◽  
Vol 51 (1-2) ◽  
pp. 31-31 ◽  
Author(s):  
Imre Bárány
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Random Polytopes

scholarly journals Periodic Billiard Trajectories in Smooth Convex Bodies

2009 ◽  
Vol 19 (2) ◽  
pp. 423-428 ◽  
Author(s):  
Roman N. Karasev
Keyword(s):  
Convex Bodies ◽  
Smooth Convex

On the illumination of smooth convex bodies

1992 ◽  
Vol 58 (6) ◽  
pp. 611-614 ◽  
Author(s):  
K�roly Bezdek
Keyword(s):  
Convex Bodies ◽  
Smooth Convex

Source radiation in the presence of smooth convex bodies

Radio Science ◽  
1979 ◽  
Vol 14 (2) ◽  
pp. 217-237 ◽  
Author(s):  
R. Mittra ◽  
S. Safavi-Naini
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Source Radiation

scholarly journals The Characteristic Properties of the Minimal Lp-Mean Width

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Tongyi Ma
Keyword(s):  
Convex Body ◽  
Existence And Uniqueness ◽  
Convex Bodies ◽  
Smooth Convex ◽  
Smooth Convex Body ◽  
Minimal Position ◽  
Mean Width ◽  
Suitable Measure ◽  
Minimum Position

Giannopoulos proved that a smooth convex body K has minimal mean width position if and only if the measure hK(u)σ(du), supported on Sn-1, is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal Lp-mean width and characterized the minimal position of convex bodies in terms of isotropicity of a suitable measure. In this paper, we study the minimal Lp-mean width of convex bodies and prove the existence and uniqueness of the minimal Lp-mean width in its SL(n) images. In addition, we establish a characterization of the minimal Lp-mean width, conclude the average Mp(K) with a variation of the minimal Lp-mean width position, and give the condition for the minimum position of Mp(K).

Random polytopes in isotropic convex bodies

2014 ◽  
pp. 357-388 ◽  
Author(s):  
Silouanos Brazitikos ◽  
Apostolos Giannopoulos ◽  
Petros Valettas ◽  
Beatrice-Helen Vritsiou
Keyword(s):  
Convex Bodies ◽  
Random Polytopes

scholarly journals Smooth convex bodies with proportional projection functions

2007 ◽  
Vol 159 (1) ◽  
pp. 317-341 ◽  
Author(s):  
Ralph Howard ◽  
Daniel Hug
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Projection Functions

Volume approximation of smooth convex bodies by three-polytopes of restricted number of edges

2007 ◽  
Vol 153 (1) ◽  
pp. 25-48 ◽  
Author(s):  
Károly J. Böröczky ◽  
Salvador S. Gomis ◽  
Péter Tick
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Restricted Number ◽  
Volume Approximation
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