Cutting the same fraction of several measures
  We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\mathbb R^d$ with a hyperplane or find a convex subset of $\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions. 
Arseniy Akopyan and Roman Karasev
math.MG math.CO