TY - JOUR
T1 - Asymptotics of perimeter-minimizing partitions
AU - Maurmann, Quinn
AU - Engelstein, Max
AU - Marcuccio, Anthony
AU - Pritchard, Taryn
PY - 2010/9
Y1 - 2010/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84866270157&partnerID=8YFLogxK
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U2 - 10.4153/CMB-2010-056-x
DO - 10.4153/CMB-2010-056-x
M3 - Article
AN - SCOPUS:84866270157
SN - 0008-4395
VL - 53
SP - 516
EP - 525
JO - Canadian Mathematical Bulletin
JF - Canadian Mathematical Bulletin
IS - 3
ER -