The Gaussian Double-Bubble Conjecture
Abstract
We establish the Gaussian Double-Bubble Conjecture: the least Gaussian-weighted perimeter way to decompose into three cells of prescribed (positive) Gaussian measure is to use a tripod-cluster, whose interfaces consist of three half-hyperplanes meeting along an -dimensional plane at angles (forming a tripod or "Y" shape in the plane). Moreover, we prove that tripod-clusters are the unique isoperimetric minimizers (up to null-sets).
Cite
@article{arxiv.1801.09296,
title = {The Gaussian Double-Bubble Conjecture},
author = {Emanuel Milman and Joe Neeman},
journal= {arXiv preprint arXiv:1801.09296},
year = {2021}
}
Comments
For publication purposes, this manuscript has been merged with our subsequent one "The Gaussian Multi-Bubble Conjecture" into a single paper entitled "The Gaussian Double-Bubble and Multi-Bubble Conjectures", which now supersedes both previous manuscripts -- see arXiv:1805.10961. To appear in Annals of Mathematics