A conformal inequality related to the conditional gauge theorem

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We prove the inequality h(x)−1 G(x, y)h(y) < cG(x, y) +c, where G is the Green function of a plane domain D, h is positive and harmonic on D, and c is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains c may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plane domains of finite area for which the constant c in the above inequality is finite.

Original languageEnglish (US)
Pages (from-to)721-733
Number of pages13
JournalTransactions of the American Mathematical Society
Volume318
Issue number2
DOIs
StatePublished - 1990

Fingerprint

Green's function
Gages
Gauge
Theorem
Harmonic

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A conformal inequality related to the conditional gauge theorem. / McConnell, Terry R.

In: Transactions of the American Mathematical Society, Vol. 318, No. 2, 1990, p. 721-733.

Research output: Contribution to journalArticle

@article{517b2cf12bef4c42abcd5ba9eb3aef73,
title = "A conformal inequality related to the conditional gauge theorem",
abstract = "We prove the inequality h(x)−1 G(x, y)h(y) < cG(x, y) +c, where G is the Green function of a plane domain D, h is positive and harmonic on D, and c is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains c may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plane domains of finite area for which the constant c in the above inequality is finite.",
author = "McConnell, {Terry R}",
year = "1990",
doi = "10.1090/S0002-9947-1990-0957083-8",
language = "English (US)",
volume = "318",
pages = "721--733",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "2",

}

TY - JOUR

T1 - A conformal inequality related to the conditional gauge theorem

AU - McConnell, Terry R

PY - 1990

Y1 - 1990

N2 - We prove the inequality h(x)−1 G(x, y)h(y) < cG(x, y) +c, where G is the Green function of a plane domain D, h is positive and harmonic on D, and c is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains c may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plane domains of finite area for which the constant c in the above inequality is finite.

AB - We prove the inequality h(x)−1 G(x, y)h(y) < cG(x, y) +c, where G is the Green function of a plane domain D, h is positive and harmonic on D, and c is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains c may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plane domains of finite area for which the constant c in the above inequality is finite.

UR - http://www.scopus.com/inward/record.url?scp=0041579895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041579895&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1990-0957083-8

DO - 10.1090/S0002-9947-1990-0957083-8

M3 - Article

AN - SCOPUS:0041579895

VL - 318

SP - 721

EP - 733

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -