On area-minimizing subgraphs in integer lattices
Combinatorics
2024-06-21 v1 Differential Geometry
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.
Cite
@article{arxiv.2406.13277,
title = {On area-minimizing subgraphs in integer lattices},
author = {Zunwu He and Bobo Hua},
journal= {arXiv preprint arXiv:2406.13277},
year = {2024}
}
Comments
39 pages, 52 figures