The Gaussian isoperimetric inequality states that if we want to partition R^n into two sets with prescribed Gaussian measure while minimizing the Gaussian surface area of the interface between the sets, then the optimal partition is obtained by cutting R^n with a hyperplane. We prove an extension to more than two parts. For example, the optimal way to partition R^3 into three parts involves cutting along three rays that meet at 120-degree angles at a common point.

Joint work with Emanuel Milman.