An isoperimetric inequality for logarithmic capacity

Roger W. Barnard, Kent Pearce, Alexander Yu Solynin

Research output: Contribution to journalArticlepeer-review

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We prove a sharp lower bound of the form cape E ≥ (1/2)diam E - ψ(area E/(1/4π diam2 E)) for the logarithmic capacity of a compact connected planar set E in terms of its area and diameter. Our lower bound includes as special cases G. Faber's inequality cap E ≥ diam 1/4 E and G. Pólya's inequality cape ≥ (area E/π)1/2. We give explicit formulations, functions of 1/2 diam E, for the extremal domains which we identify.

Original languageEnglish
Pages (from-to)419-436
Number of pages18
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Issue number2
StatePublished - 2002


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