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<p>A version of the isoperimetric inequality holds for a function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>f</mi> </math></EquationSource> </InlineEquation>for which log <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(|f|\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>f</mi> <mo stretchy="false">|</mo> </mrow> </math></EquationSource> </InlineEquation> is subharmonic. We characterize a subclass of harmonic functionswhich has these properties. For the class of functions <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(h(z_1, \ldots ,z_n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo stretchy="false">(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(z_i \in \mathbb{U}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>∈</mo> <mi mathvariant="double-struck">U</mi> </mrow> </math></EquationSource> </InlineEquation>, whichseparately have these properties, we prove a version of isoperimetric inequality.In addition, we prove a version of Gabriel’s theorem for the subclass of harmonicfunctions.</p>

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Isoperimetric inequality for harmonic functions

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • M. Mateljević,
  • B. Purtić

摘要

A version of the isoperimetric inequality holds for a function \(f\) f for which log \(|f|\) | f | is subharmonic. We characterize a subclass of harmonic functionswhich has these properties. For the class of functions \(h(z_1, \ldots ,z_n)\) h ( z 1 , … , z n ) , \(z_i \in \mathbb{U}\) z i ∈ U , whichseparately have these properties, we prove a version of isoperimetric inequality.In addition, we prove a version of Gabriel’s theorem for the subclass of harmonicfunctions.