A RELATIVE ISOPERIMETRIC INEQUALITY

We prove that, if Ω is an open subset of ℝN with finite measure, there exists a hyperplane H through 0 such that the measure of Ω ∩ H is less than the measure of B ∩ H, where B is the open ball with center 0 having the same measure as Ω. An application is given to the optimal Poincaré inequality on BV(Ω).