English

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

R2 v1 2026-06-22T02:08:40.794Z