It asserts that there exists a universal constant c such that for any convex set K of unit volume in any dimension, there exists a hyperplane H passing through its centroid such that the volume of the section K ∩ H is bounded below by c.
Mar 24, 2014 · Basically it says that the maximal hyperplane section of any convex body cannot be really small compare to its volume. For me, it looks ...
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The hyperplane conjecture is a major unsolved problem in high-dimensional convex geometry that has attracted much attention in the geometric and functional ...
Dec 18, 2006 · Abstract: Let N > n, and denote by K the convex hull of N independent standard gaussian random vectors in an n-dimensional Euclidean space.
In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space. There are several rather similar ...
In [60] it is proven that Question 2.1 has an affirmative answer if and only if Bourgain's hyperplane conjecture holds true. 3 Distribution of volume in convex ...
Abstract. We introduce a conjecture that we call the Two Hyperplane Conjecture, saying that an isoperimetric surface that divides a convex body in half by ...
Dec 18, 2006 · The hyperplane conjecture suggests a positive answer to the following question: Is there a universal constant c > 0, such that for any ...
The hyperplane conjecture suggests a positive answer to the following question: Is there a universal constant c > 0, such that for any dimension n and for ...
We describe four related open problems in asymptotic geometric analysis: the hyperplane con- jecture, the isotropic constant conjecture, Sylvester's problem, ...