Harmonic Dirichlet Functions on Planar Graphs
Discrete & Computational Geometry(2019)
摘要
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 in a domain D , there is a canonical, explicit bounded linear isomorphism between the space of harmonic Dirichlet functions on T and the space of harmonic Dirichlet functions on D .
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关键词
Circle packing, Planar graphs, Harmonic functions, Dirichlet space, Electrical networks
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