English

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

R2 v1 2026-06-28T17:11:38.693Z