Calculus of Variations and Geometric Measure Theory
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E. Paolini - V. M. Tortorelli

The quadruple planar bubble enclosing equal areas is symmetric

created by paolini on 05 Nov 2018
modified on 08 Nov 2018

[BibTeX]

Preprint

Inserted: 5 nov 2018
Last Updated: 8 nov 2018

Year: 2018

Abstract:

In this paper we make the final step in finding the optimal way to enclose and separate four planar regions with equal area. In (9) the graph-topology of the optimal cluster was found reducing the set of candidates to a one-parameter family of different clusters. With a simple argument we show that the minimal set has a further simmetry and hence is uniquely determined up to isometries.


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