Complete quasiconvex mappings in polydisc. (English) Zbl 1222.32031
Front. Math. China 1, No. 1, 120-129 (2006); translation from Chin. Ann. Math., Ser. A 25, No. 1, 105-112 (2004).
This is a translation from [Chin. Ann. Math., Ser. A 25, No. 1, 105–112 (2004; Zbl 1056.32016)].
Summary: A class of biholomorphic mappings called complete quasiconvex mappings is introduced and studied in bounded convex Reinhardt domains of \(\mathbb C^{ n }\). Through a detailed analysis of the analytic characterization for this class of mappings, it is shown that this class of mappings contains the convex mappings and is also a subset of the class of starlike mappings. In the special case of the polydisc, a decomposition theorem is established for the complete quasiconvex mappings, which in turn is used to derive an improved sufficient condition for the convex mappings.
Summary: A class of biholomorphic mappings called complete quasiconvex mappings is introduced and studied in bounded convex Reinhardt domains of \(\mathbb C^{ n }\). Through a detailed analysis of the analytic characterization for this class of mappings, it is shown that this class of mappings contains the convex mappings and is also a subset of the class of starlike mappings. In the special case of the polydisc, a decomposition theorem is established for the complete quasiconvex mappings, which in turn is used to derive an improved sufficient condition for the convex mappings.
MSC:
| 32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
Keywords:
bounded convex Reinhardt domain; complete quasiconvex mapping; quasiconvex mapping; convex mapping; decomposition theoremCitations:
Zbl 1056.32016References:
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