A note on Bourgain-Milman's universal constant
  The present note is a result of an on-going investigation into the logarithmic Brunn-Minkowski inequality. We obtain lower estimates on the volume product for convex bodies in $\mathbb{R}^n$ not necessarily symmetric with respect to the origin from a modified logarithmic Brunn-Minkowski inequality. 
Alina Stancu
math.MG math.DG