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...

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Differential Geometry