Harmonic Dirichlet Functions on Planar Graphs
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Hutchcroft, T https://orcid.org/0000-0003-0061-593X
Abstract
Benjamini and Schramm (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
Description
Keywords
Circle packing, Planar graphs, Harmonic functions, Dirichlet space, Electrical networks
Journal Title
Discrete and Computational Geometry
Conference Name
Journal ISSN
0179-5376
1432-0444
1432-0444
Volume Title
61
Publisher
Springer Science and Business Media LLC
Publisher DOI
Sponsorship
Microsoft Research