arXiv Analytics

Sign in

arXiv:1311.4012 [math.DG]AbstractReferencesReviewsResources

Proof of the Log-Convex Density Conjecture

Gregory R. Chambers

Published 2013-11-16, updated 2015-03-15Version 3

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.

Comments: 40 pages, 7 figures
Categories: math.DG
Subjects: 49Q20, 53C17
Related articles:
arXiv:1107.4402 [math.DG] (Published 2011-07-22, updated 2014-12-22)
The Log-Convex Density Conjecture and vertical surface area in warped products
arXiv:math/0602135 [math.DG] (Published 2006-02-07)
On the isoperimetric problem in Euclidean space with density

Links

Toolbox