Harmonic Dirichlet Functions on Planar Graphs
Harmonic Dirichlet Functions on Planar Graphs
Benjamini and Schramm (Invent Math 126(3):565–587, 1996) used circle packing to prove that every transient, bounded degree planar graph admits non-constant harmonic functions of finite Dirichlet energy. We refine their result, showing in particular that for every transient, bounded degree, simple planar triangulation T and every circle packing of T …