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 08 Jul 2017



Inserted: 20 jul 2016
Last Updated: 8 jul 2017

Year: 2016

ArXiv: 1612.00178 PDF


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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