Document Zbl 0713.30014

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The singular-leaf criterion on the circle ring domain. (Chinese. English summary) Zbl 0713.30014

Acta Sci. Nat. Univ. Pekin. 25, No. 5, 527-536 (1989).

It is proved in this paper that the ring domain \(A_ r=\{z:1<| z| <r\}\) is a (\(\alpha\),\(\beta\))-uniform domain with explicit upper bounds for \(\alpha\) and \(\beta\). A sufficient condition that a locally univalent analytic function is univalent in the whole domain \(A_ r\) is given. These results are related to the work by K. Astala and F. W. Gehring [Complex Variables, Theory Appl. 3, 45-54 (1984; Zbl 0588.30022)].

Reviewer: Li Zhong

MSC:

30C62

Quasiconformal mappings in the complex plane

Keywords:

uniform domain

Citations:

Zbl 0588.30022

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