Double and Multiple Bubbles in Gauss Space’

In 2002 my coauthors and I proved that the familiar double bubble is the least-perimeter way to enclose and separate two given volumes in R^3. In 2008 Ben Reichardt extended the result to R^n. After ten years of no further progress, Milman and Neeman have announced an extension to Gauss space (R^n with Gaussian density). Their work applies not just to double bubbles but to all multiple bubbles in dimensions high enough to easily accommodate them. Although the proof is difficult, the solution and some of the main ideas are easy to describe. We’ll also discuss some open questions and recent results for other densities.