Published April 2019
| Published + Accepted Version
Journal Article
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Harmonic Dirichlet functions on planar graphs
- Creators
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Hutchcroft, Tom
Abstract
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.
Additional Information
© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Received: 26 July 2017 / Revised: 24 October 2018 / Accepted: 7 January 2019 / Published online: 30 January 2019. The author was supported by a Microsoft Research PhD Fellowship. We thank the anonymous referees for their comments and corrections.Attached Files
Published - Hutchcroft2019_Article_HarmonicDirichletFunctionsOnPl.pdf
Accepted Version - 1707.07751.pdf
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Additional details
- Eprint ID
- 111007
- Resolver ID
- CaltechAUTHORS:20210922-193309575
- Microsoft Research
- Created
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2021-09-27Created from EPrint's datestamp field
- Updated
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2021-09-27Created from EPrint's last_modified field