UNSPECIFIED (2002) Extremal problems for quasiconformal maps of punctured plane domains. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 354 (4). pp. 1631-1650. ISSN 0002-9947

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Abstract

The main goal of this paper is to give an affirmative answer to the long-standing conjecture which asserts that the affine map is a uniquely extremal quasiconformal map in the Teichmuller space of the complex plane punctured at the integer lattice points. In addition we derive a corollary related to the geometry of the corresponding Teichmuller space. Besides that we consider the classical dual extremal problem which naturally arises in the tangent space of the Teichmuller space. In particular we prove the uniqueness of Hahn-Banach extension of the associated linear functional given on the Bergman space of the integer lattice domain. Several useful estimates related to the local and global properties of integrable meromorphic functions and the delta functional (see the definition below) are also obtained. These estimates are intended to study the behavior of integrable functions near singularities and they are valid in general settings.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Publisher:	AMER MATHEMATICAL SOC
ISSN:	0002-9947
Date:	2002
Volume:	354
Number:	4
Number of Pages:	20
Page Range:	pp. 1631-1650
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/11352

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