The Gaussian Double-Bubble Conjecture

Abstract

We establish the Gaussian Double-Bubble Conjecture: the least Gaussian-weighted perimeter way to decompose ${\mathbb{R}}^n$ into three cells of prescribed (positive) Gaussian measure is to use a tripod-cluster, whose interfaces consist of three half-hyperplanes meeting along an $(n-2)$-dimensional plane at $120^{\circ }$ 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).

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

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