Local Minimality Results Related to the Bloch and Landau Constants

Albert Baernstein () and Jade P. Vinson ()
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Albert Baernstein: Washington University
Jade P. Vinson: Washington University

A chapter in Quasiconformal Mappings and Analysis, 1998, pp 55-89 from Springer

Abstract: Abstract Let H( $$ \left( \mathbb{D} \right)$$ ) denote the set of functions holomorphic in the unit disk $$ \mathbb{D} \subset \mathbb{C}.$$ The theorem of Bloch, [Bh] from 1925, asserts existence of an absolute constant B such that for each $$ f \in H\left( \mathbb{D} \right)$$ there is a disk of radius $$B|f'\left( 0 \right)| $$ which is the one-one image under f of some subdomain of $$ \left( \mathbb{D} \right)$$ Such a disk is called a “schlicht disk” for f. The best, i.e., largest, value of B is called Bloch’s constant.

Keywords: Discrete Subset; Complex Dilatation; Hyperbolic Metrics; Hyperbolic Triangle; Hyperbolic Geodesic (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4612-0605-7_7

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