Proof of the Log-Convex Density Conjecture

15 Mar 2015 · Chambers Gregory R. ·

We completely characterize isoperimetric regions in R^n with density e^h, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the Log-Convex Density Conjecture due to Kenneth Brakke.