| Issue |
ESAIM: COCV
Volume 24, Number 3, July–September 2018
|
|
|---|---|---|
| Page(s) | 1303 - 1331 | |
| DOI | https://doi.org/10.1051/cocv/2017066 | |
| Published online | 13 September 2018 | |
Minimal clusters of four planar regions with the same area ★
1
Dipartimento di Matematica,
Largo Bruno Pontecorvo 5,
Università di Pisa, Italy
2
Dipartimento di Matematica e Informatica “U. Dini”,
Viale Morgagni 67/a,
Università degli Studi di Firenze, Italy
* Corresponding author: emanuele.paolini@unipi.it
Received:
27
April
2017
Accepted:
30
September
2017
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.
Mathematics Subject Classification: 53A10 / 49Q05 / 52C99
Key words: Minimal clusters / planar networks
© EDP Sciences, SMAI 2018
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