JournalsjemsVol. 21, No. 8pp. 2301–2332

Proof of the Log-Convex Density Conjecture

  • Gregory R. Chambers

    Rice University, Houston, USA
Proof of the Log-Convex Density Conjecture cover
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Abstract

We completely characterize isoperimetric regions in Rn\mathbb R^n with density ehe^h, where hh 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.

Cite this article

Gregory R. Chambers, Proof of the Log-Convex Density Conjecture. J. Eur. Math. Soc. 21 (2019), no. 8, pp. 2301–2332

DOI 10.4171/JEMS/885