On area-minimizing subgraphs in integer lattices
arXiv:2406.13277
Abstract
We introduce area-minimizing subgraphs in an infinite graph via the formulation of functions of bounded variations initiated by De Giorgi. We classify area-minimizing subgraphs in the two-dimensional integer lattice up to isomorphisms, and prove general geometric properties for those in high-dimensional cases.
39 pages, 52 figures