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Every planar graph with the Liouville pr...

Carmesin, Johannes...

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Every planar graph with the Liouville property is amenable by Carmesin, Johannes ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	01-01-2015
Summary	We introduce a strengthening of the notion of transience for planar maps in order to relax the standard condition of bounded degree appearing in various results, in particular, the existence of Dirichlet harmonic functions proved by Benjamini and Schramm. As a corollary we obtain that every planar non-amenable graph admits Dirichlet harmonic functions.
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1502.02542

Citation

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AMA 11th EditionReferences

Carmesin, Johannes. Every planar graph with the Liouville property is amenable. N.A. January 01, 2015. Accessed October 03, 2025. https://online.provdatabase.com/cite/18344

APA 7th EditionReferences

Carmesin, Johannes. (2015). Every planar graph with the Liouville property is amenable. N.A. https://online.provdatabase.com/cite/18344

Chicago 17th EditionReferences

Carmesin, Johannes. Every planar graph with the Liouville property is amenable. N.A. 2015. https://online.provdatabase.com/cite/18344

HarvardReferences

Carmesin, Johannes. (2015). Every planar graph with the Liouville property is amenable. [Online]. N.A. Available from: https://online.provdatabase.com/cite/18344. (Accessed 03 October 2025).

Harvard AustraliaReferences

Carmesin, Johannes, 2015, Every planar graph with the Liouville property is amenable, N.A, viewed 03 October 2025, <https://online.provdatabase.com/cite/18344>

MLA 9th EditionWorks Cited

Carmesin, Johannes. Every planar graph with the Liouville property is amenable. N.A, 2015. PROV Database, https://online.provdatabase.com/cite/18344.

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