Calculus of Variations and Geometric Measure Theory
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E. Paolini - A. Tamagnini

Minimal clusters of four planar regions with the same area

created by tamagnini on 20 Jul 2016
modified by paolini on 25 Oct 2018


Published Paper

Inserted: 20 jul 2016
Last Updated: 25 oct 2018

Journal: ESAIM: COCV
Volume: 24
Number: 3
Pages: 1303-1331
Year: 2018
Doi: 10.1051/cocv/2017066

ArXiv: 1612.00178v2 PDF
Links: article in journal


We prove that the optimal way to enclose and separate four planar regions with equal area using the less possible perimeter requires all regions to be connected. Moreover, the topology of such optimal clusters is uniquely determined.

Keywords: minimal cluster, bubbles


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