Minimal clusters of four planar regions with the same area

Author:

Paolini EmanueleORCID,Tamagnini AndreaORCID

Abstract

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.

Publisher

EDP Sciences

Subject

Computational Mathematics,Control and Optimization,Control and Systems Engineering

Reference24 articles.

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2. Bandle C., Isoperimetric Inequalities and Applications. In Vol. 7 of Monographs and Studies in Mathematics. Pitman Publishing (1980)

3. Blaschke W., Kreis und Kugel. Leipzig (1916)

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