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Inequalities for the Gamma Function and estimates for the volume of sections of $B_p^n$

Jesus Bastero·Fernando Galve·Ana Pena·Miguel Romance
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Abstract

We consider $k$-dimensional central sections of the unit ball of $\ell_p^n$ (denoted $B_p^n$) and we prove that their volume are bounded by the volume of $B_p^n$ whenever $1<p<2$ and $1\le k\le (n-1)/2$ or $k=n-1$. We also consider $0<p<1$ and other cases. We obtain sharp inequalities involving Gamma Function in order to get these results.

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Jesus Bastero, Fernando Galve, Ana Pena, Miguel Romance. 2000-08-01. Inequalities for the Gamma Function and estimates for the volume of sections of $B_p^n$. https://arxiv.org/abs/math/0008007

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