科研之友
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摘要
For n is an element of N, let S-n be the smallest number S > 0 satisfying the inequality
integral(K) f <= S . vertical bar K vertical bar(1/n). max(xi is an element of Sn-1) integral(K boolean AND xi perpendicular to) f
for all centrally-symmetric convex bodies K in R-n and all even, continuous probability densities f on K. Here vertical bar K vertical bar is the volume of K. It was proved in [16] that S-n <= 2 root n, and in analogy with Bourgain's slicing problem, it was asked whether S-n is bounded from above by a universal constant. In this note we construct an example showing that S-n >= c root n/root log log n, where c > 0 is an absolute constant. Additionally, for any 0 < alpha < 2 we describe a related example that satisfies the so-called psi(alpha)-condition.
- 出版日期2018-4-1
