Proof of the Log-Convex Density Conjecture

Gregory R. Chambers

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arXiv · 1311.4012

Proof of the Log-Convex Density Conjecture

Gregory R. Chambers

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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.

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Gregory R. Chambers. 2013-11-16. Proof of the Log-Convex Density Conjecture. https://arxiv.org/abs/1311.4012

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