Resumen de Asymptotics of Perimeter-Minimizing Partitions

Quinn Maurmann, Max Engelstein, Anthony Marcuccio, Taryn Pritchard

• 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.