Geodesic
Asymptotics of Perimeter-Minimizing Partitions
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 516-525

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DOI

We prove that the least perimeter $P(n)$ of a partition of a smooth, compact Riemannian surface into $n$ regions of equal area $A$ is asymptotic to $n/2$ times the perimeter of a planar regular hexagon of area $A$ . Along the way, we derive tighter estimates for flat tori, Klein bottles, truncated cylinders, and Möbius bands.
DOI : 10.4153/CMB-2010-056-x
Mots-clés : 53C42 
Maurmann, Quinn; Engelstein, Max; Marcuccio, Anthony; Pritchard, Taryn. Asymptotics of Perimeter-Minimizing Partitions. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 516-525. doi: 10.4153/CMB-2010-056-x
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     title = {Asymptotics of {Perimeter-Minimizing} {Partitions}},
     journal = {Canadian mathematical bulletin},
     pages = {516--525},
     year = {2010},
     volume = {53},
     number = {3},
     doi = {10.4153/CMB-2010-056-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-056-x/}
}
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