Geodesic
On a problem of Avhadiev
Lobachevskii journal of mathematics, Tome 16 (2004), pp. 57-69
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In this paper we consider a lower estimate for the ratio $I(\Omega)$ of the conformal moment of a simple connected domain $\Omega$ in the complex plane to the moment of inertia of this domain about its boundary. Related functionals depending on a simple connected domain $\Omega$ and two points $\omega_1,\omega_2\in\Omega$ with fixed hyperbolical distance between them are estimated. As a consequence a nontrivial lower estimate for $I(\Omega)$ is obtained.
Keywords: moment of inertia of domain about its boundary, univalent functions.
Mots-clés : conformal moment of domain 
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A. A. Kuznetsov. On a problem of Avhadiev. Lobachevskii journal of mathematics, Tome 16 (2004), pp. 57-69. http://geodesic.mathdoc.fr/item/LJM_2004_16_a2/

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