Inequalities for the Gamma Function and estimates for the volume of   sections of $B_p^n$
  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. 
Jesus Bastero (Univ. of Zaragoza), Fernando Galve (Univ. of Zaragoza),   Ana Pena (Univ. of Zaragoza), Miguel Romance (Univ....