# Minimal cluster computation for four planar regions with the same area

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### "Minimal cluster computation for fou..." refers background or methods in this paper

...For N ≥ 1 first existence and partial regularity in Rn was given by Almgren [1] while Taylor [12] describes the singularities for minimizers in R3....

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...For N ≥ 1 rst existence and partial regularity in Rn was given by Almgren [1] while Taylor [12] describes the singularities for minimizers inR(3)....

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...In particular the structure of minimal cluster has been widely studied when the ambient space isR(2) (see [6]) orR(3) (see [12])....

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343 citations

### "Minimal cluster computation for fou..." refers background or methods in this paper

...For N ≥ 1 first existence and partial regularity in Rn was given by Almgren [1] while Taylor [12] describes the singularities for minimizers in R3....

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...The following result gives the existence of minimal clusters (see [1], [6] and [4])....

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...For N ≥ 1 rst existence and partial regularity in Rn was given by Almgren [1] while Taylor [12] describes the singularities for minimizers inR(3)....

[...]

202 citations

### "Minimal cluster computation for fou..." refers background in this paper

...The following result gives the existence of minimal clusters (see [1], [6] and [4])....

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...Existence and regularity of minimizers inR(2) was proved byMorgan [6] (see also [4]): the regions of a minimizer inR(2) are delimited by a nite number of circular arcs which meet in triples at their end-points....

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101 citations

### "Minimal cluster computation for fou..." refers background in this paper

...[2] proved that for N = 2 inR(2) the two regions of anyminimizer are delimited by three circular arcs joining in two points (standard double bubble) and are uniquely determined by their enclosed areas....

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...theminimal clusterswith two regions, see [2]) can be obtained, up to rescaling, by projecting the geodesic network on the sphere given by three meridians joining in two antipodal points with equal angles of 120 degrees....

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