Isoperimetric inequality, F. Gehring’s problem on linked curves and capacity

Mateljević, Miodrag

doi:10.2298/fil1503629m

Cited by 3 publications

(3 citation statements)

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“…The analytic proof of the isoperimetric inequality is exposed in [32], see also [19], [20], [21]. For a discussion on (4.3), various connections with some known analytic inequalities (including Carleman's one), we refer to the survey article [24] of Osserman.…”

Section: 2mentioning

confidence: 99%

Sharp inequalities over the unit polydisc

Markovic

2015

Journal of Functional Analysis

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Abstract. Motivated by some results due to Burbea we prove that if a certain sharp integral inequality holds for functions in the unit polydisc which belong to concrete Hardy spaces, then it also holds, in an appropriate form, in the case of functions from arbitrary Hardy spaces. We also examine the equality case. We present an application of this main result to a Burbea inequality which includes an isoperimetric type inequality as a special case.

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Section: 2mentioning

confidence: 99%

Sharp inequalities over the unit polydisc

Markovic

2015

Journal of Functional Analysis

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“…The inequality (4.2) is related to the classical isoperimetric inequality: If D is a simply-connected domain in the plain such that ∂D is a rectifiable curve, then the area of D and the length of ∂D satisfy with equality if and only if D is a disc. The analytic proof of the isoperimetric inequality is exposed in [32], see also [19], [20], [21]. For a discussion on (4.3), various connections with some known analytic inequalities (including Carleman's one), we refer to the survey article [24] of Osserman.…”

Section: Equality Attains If and Only If Eithermentioning

confidence: 99%

Sharp inequalities over the unit polydisc

Markovic¹

2014

Preprint

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Motivated by some results due to Burbea we prove that if a certain sharp integral inequality holds for functions in the unit polydisc which belong to concrete Hardy spaces, then it also holds, in an appropriate form, in the case of functions from arbitrary Hardy spaces. We also examine the equality case. We present an application of this main result to a Burbea inequality which includes an isoperimetric type inequality as a special case.

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“…and that the equality holds if and only if the curve is a circle. Dozens of proofs of the isoperimetric inequality have been found, see for example [3,8,15,16,20,39,48,59,60] and the literature cited there. In particular we highly recommend Expository Lectures by Andrejs Treibergs, [59,60], to the interested reader as introduction in the subject, and more advanced Lectures by Druet [15] and Fusco [20].…”

Section: Introductionmentioning

confidence: 99%