We investigate the Edge-Isoperimetric Problem (EIP) for sets with n elements of the cubic lattice by emphasizing its relation with the emergence of the Wulff shape in the crystallization problem. The exponent 3/4 is optimal. This extends to the cubic lattice analogous results that have already been established for the triangular, the hexagonal, and the square lattice in two space dimensions.
N-3/4 Law in the cubic lattice
U Stefanelli
2019
Abstract
We investigate the Edge-Isoperimetric Problem (EIP) for sets with n elements of the cubic lattice by emphasizing its relation with the emergence of the Wulff shape in the crystallization problem. The exponent 3/4 is optimal. This extends to the cubic lattice analogous results that have already been established for the triangular, the hexagonal, and the square lattice in two space dimensions.File in questo prodotto:
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Descrizione: N-3/4 Law in the cubic lattice
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