Proof of the Log-Convex Density Conjecture
Differential Geometry
2015-03-17 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1311.4012,
title = {Proof of the Log-Convex Density Conjecture},
author = {Gregory R. Chambers},
journal= {arXiv preprint arXiv:1311.4012},
year = {2015}
}
Comments
40 pages, 7 figures