Dimension Reduction in $L_p$, $0<p<2$
  Complementing a recent observation of Newman and Rabinovich for $p=1$ we observe here that for all $0<p<2$ any $k$ points in $L_p$ embeds with distortion $(1+\e)$ into $\ell_p^n$ where $n$ is linear in $k$ (and polynomial in $\e^{-1}$). 
Gideon Schechtman
math.MG math.FA