Hutchcroft, Tom (2019) Harmonic Dirichlet functions on planar graphs. Discrete & Computational Geometry, 61 (3). pp. 479-506. ISSN 0179-5376. doi:10.1007/s00454-019-00057-2. https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309575
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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.
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| 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. | |||||||||
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| Subject Keywords: | Circle packing · Planar graphs · Harmonic functions · Dirichlet space · Electrical networks | |||||||||
| Issue or Number: | 3 | |||||||||
| DOI: | 10.1007/s00454-019-00057-2 | |||||||||
| Record Number: | CaltechAUTHORS:20210922-193309575 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309575 | |||||||||
| Official Citation: | Hutchcroft, T. Harmonic Dirichlet Functions on Planar Graphs. Discrete Comput Geom 61, 479–506 (2019). https://doi.org/10.1007/s00454-019-00057-2 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 111007 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 27 Sep 2021 18:42 | |||||||||
| Last Modified: | 27 Sep 2021 18:42 |
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