Proof of the double bubble conjecture in \(\mathbb{R}^4\) and certain higher dimensional cases.
type: Item
instance of: scholarly article
title: Proof of the double bubble conjecture in \(\mathbb{R}^4\) and certain higher dimensional cases.
zbMATH Open document ID: 1056.53007
author: Ben Reichardt
author: Cory Heilmann
author: Yuan Y. Lai
author: Anita Spielman
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: The standard double bubble is, by now, one of the most familiar and controversal objects in the `\(n\)-dimensional soap bubble domain'. As most scientists know, the standard double bubble consists of three spherical caps meeting at 120 degree angles, and it is conjectured as the least-area hypersurface that encloses two given volumes in \(\mathbb R^n\). The case \(n=3\), solved in 2000 by another team of four mathematicians, is now a very well known result. The four authors of the present study prove the conjecture for \(n=4\), and open some important directions towards higher dimensions. The arguments are well organized and easy to follow, making this report accessible to a large audience of mathematicians, including graduate students.
reviewed by: Magdalena Daniela Toda
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 2101056
zbMATH Keywords: double bubble
zbMATH Keywords: root stability
zbMATH Keywords: leaf stability
Wikidata QID: Q123363095
MaRDI profile type: Publication
full work available at URL: pjm.2003.208.347
OpenAlex ID: W2088591516
DOI: 10.2140/PJM.2003.208.347
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description: scientific article; zbMATH DE number 2101056