scholarly journals Further Unifying Two Approaches to the Hyperplane Conjecture

2012 ◽  
Vol 2014 (6) ◽  
pp. 1493-1514 ◽  
Author(s):  
Beatrice-Helen Vritsiou
Keyword(s):  
Hyperplane Conjecture

Hyperplane conjecture and Bourgain’s upper bound

2014 ◽  
pp. 103-137
Author(s):  
Silouanos Brazitikos ◽  
Apostolos Giannopoulos ◽  
Petros Valettas ◽  
Beatrice-Helen Vritsiou
Keyword(s):  
Upper Bound ◽  
Hyperplane Conjecture

scholarly journals On the hyperplane conjecture for random convex sets

2009 ◽  
Vol 170 (1) ◽  
pp. 253-268 ◽  
Author(s):  
Bo’az Klartag ◽  
Gady Kozma
Keyword(s):  
Convex Sets ◽  
Hyperplane Conjecture ◽  
Random Convex

scholarly journals The Two Hyperplane Conjecture

2019 ◽  
Vol 35 (6) ◽  
pp. 728-748
Author(s):  
David Jerison
Keyword(s):  
Hyperplane Conjecture

scholarly journals Concentration between Lévy’s inequality and the Poincaré inequality for log-concave densities

2018 ◽  
Vol 20 (05) ◽  
pp. 1750068
Author(s):  
Erez Buchweitz
Keyword(s):  
Isoperimetric Inequality ◽  
Random Vector ◽  
Poincaré Inequality ◽  
Poincare Inequality ◽  
Strong Concentration ◽  
The Third ◽  
Vector Formula ◽  
Hyperplane Conjecture

Given a suitably normalized random vector [Formula: see text], we observe that the function [Formula: see text], defined for [Formula: see text], admits surprisingly strong concentration far surpassing what is expected on account of Lévy’s isoperimetric inequality. Among the measures to which the above holds are all log-concave measures, for which a solution of the similar problem concerning the third marginal moments [Formula: see text] would imply the hyperplane conjecture.

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