Calculus of Variations and Geometric Measure Theory

E. Paolini - V. M. Tortorelli

The quadruple planar bubble enclosing equal areas is symmetric

created by paolini on 05 Nov 2018
modified on 02 Mar 2021


Published Paper

Inserted: 5 nov 2018
Last Updated: 2 mar 2021

Journal: Calc. Var.
Volume: 59
Number: 1
Year: 2020
Doi: 10.1007/s00526-019-1687-9
Links: journal, read only pdf


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.