On the volume of the intersection of two $L_p^n$ balls

Details On the volume of the intersection of two $L_p^n$ balls On the volume of the intersection of two $L_p^n$ balls

1989-11-09

arxiv.org/abs/math/9201206v1

Mathematics

Functional Analysis

Scientific paper

This note deals with the following problem, the case $p=1$, $q=2$ of which was introduced to us by Vitali Milman: What is the volume left in the $L_p^n$ ball after removing a t-multiple of the $L_q^n$ ball? Recall that the $L_r^n$ ball is the set $\{(t_1,t_2,\dots,t_n);\ t_i\in{\bf R},\ n^{-1}\sum_{i=1}^n|t_i|^r\le 1\}$ and note that for $0

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