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arXiv · 1901.05868

Isoperimetric inequalities for Bergman analytic content

Stephen J. Gardiner·Marius Ghergu·Tomas Sjödin
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Abstract

The Bergman $p$-analytic content ($1\leq p<\infty $) of a planar domain $\Omega $ measures the $L^{p}(\Omega )$-distance between $\overline{z}$ and the Bergman space $A^{p}(\Omega )$ of holomorphic functions. It has a natural analogue in all dimensions which is formulated in terms of harmonic vector fields. This paper investigates isoperimetric inequalities for Bergman $p$-analytic content in terms of the St Venant functional for torsional rigidity, and addresses the cases of equality with the upper and lower bounds.

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Stephen J. Gardiner, Marius Ghergu, Tomas Sjödin. 2019-01-17. Isoperimetric inequalities for Bergman analytic content. https://arxiv.org/abs/1901.05868

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