A DISCRETE HARMONIC FUNCTION BOUNDED ON A LARGE PORTION OF Z2 IS CONSTANT

Lev Buhovsky; Alexander Logunov; Eugenia Malinnikova; Mikhail Sodin

doi:10.1215/00127094-2021-0037

A DISCRETE HARMONIC FUNCTION BOUNDED ON A LARGE PORTION OF Z² IS CONSTANT

Lev Buhovsky, Alexander Logunov, Eugenia Malinnikova, Mikhail Sodin

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

An improvement of the Liouville theorem for discrete harmonic functions on Z² is obtained. More precisely, we prove that there exists a positive constant " such that if u is discrete harmonic on Z² and for each sufficiently large square Q centered at the origin \ u\ ≤ 1 on a (1 − ε ) portion of Q, then u is constant.

Original language	English
Pages (from-to)	1349-1378
Number of pages	30
Journal	Duke Mathematical Journal
Volume	171
Issue number	6
DOIs	https://doi.org/10.1215/00127094-2021-0037
State	Published - 15 Apr 2022

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1215/00127094-2021-0037

Cite this

@article{5d0385f0020346d98468c125f8a362ab,

title = "A DISCRETE HARMONIC FUNCTION BOUNDED ON A LARGE PORTION OF Z2 IS CONSTANT",

abstract = "An improvement of the Liouville theorem for discrete harmonic functions on Z2 is obtained. More precisely, we prove that there exists a positive constant {"} such that if u is discrete harmonic on Z2 and for each sufficiently large square Q centered at the origin \textbackslash{} u\textbackslash{} ≤ 1 on a (1 − ε ) portion of Q, then u is constant.",

author = "Lev Buhovsky and Alexander Logunov and Eugenia Malinnikova and Mikhail Sodin",

note = "Publisher Copyright: {\textcopyright} 2022",

year = "2022",

month = apr,

day = "15",

doi = "10.1215/00127094-2021-0037",

language = "الإنجليزيّة",

volume = "171",

pages = "1349--1378",

journal = "Duke Mathematical Journal",

issn = "0012-7094",

publisher = "Duke University Press",

number = "6",

}

TY - JOUR

T1 - A DISCRETE HARMONIC FUNCTION BOUNDED ON A LARGE PORTION OF Z2 IS CONSTANT

AU - Buhovsky, Lev

AU - Logunov, Alexander

AU - Malinnikova, Eugenia

AU - Sodin, Mikhail

PY - 2022/4/15

Y1 - 2022/4/15

N2 - An improvement of the Liouville theorem for discrete harmonic functions on Z2 is obtained. More precisely, we prove that there exists a positive constant " such that if u is discrete harmonic on Z2 and for each sufficiently large square Q centered at the origin \ u\ ≤ 1 on a (1 − ε ) portion of Q, then u is constant.

AB - An improvement of the Liouville theorem for discrete harmonic functions on Z2 is obtained. More precisely, we prove that there exists a positive constant " such that if u is discrete harmonic on Z2 and for each sufficiently large square Q centered at the origin \ u\ ≤ 1 on a (1 − ε ) portion of Q, then u is constant.

UR - http://www.scopus.com/inward/record.url?scp=85130260882&partnerID=8YFLogxK

U2 - 10.1215/00127094-2021-0037

DO - 10.1215/00127094-2021-0037

M3 - مقالة

SN - 0012-7094

VL - 171

SP - 1349

EP - 1378

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 6

ER -

A DISCRETE HARMONIC FUNCTION BOUNDED ON A LARGE PORTION OF Z² IS CONSTANT

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this