A discrete harmonic function bounded on a large portion of \({\mathbb{Z}^2}\) is constant

DOI10.1215/00127094-2021-0037zbMath1494.31002arXiv1712.07902OpenAlexW4226333864MaRDI QIDQ2130507

Lev Buhovsky, Alexander Logunov, Eugenia Malinnikova, Mikhail Sodin

Publication date: 25 April 2022

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.07902

zbMATH Keywords

Liouville's theoremdiscrete harmonic functionsthree-spheres theorem

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items

Anderson-Bernoulli localization at large disorder on the 2D lattice, Uniqueness results for solutions of continuous and discrete PDE, On (global) unique continuation properties of the fractional discrete Laplacian, Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice

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