Abstract

BECKER, Jochen  and  POMMERENKE, Christian. On analytic families of conformai maps. Rev.colomb.mat. [online]. 2017, vol.51, n.1, pp.15-19. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v51n1.66832.

Let Λ be a domain in ℂ and let ... be meromorphic in We assume that is holomorphic in for fixed z.

The main theorem states: Let Λ 0 be a subdomain of Λ such that f λ is univalent in for . If has a quasiconformal extension to the closure of for one then f λ has a quasiconformal extension for all .

This result is related to a theorem of Mañé, Sad and Sullivan (1983) where the assumptions are however different. The main tool of our proof is the Grunsky inequality for univalent functions.

Keywords : Univalent function; quasiconformal extension; analytic parameter; Grunsky inequality.

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