Rigidity for convex mappings of Reinhardt domains and its applications
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摘要:
In this paper,we investigate rigidity and its applications to extreme points of biholomorphic convex mappings on Reinhardt domains.By introducing a version of the scaling method,we precisely construct many unbounded convex mappings with only one infinite discontinuity on the boundary of this domain.We also give a rigidity of these unbounded convex mappings via the Kobayashi metric and the Liouville-type theorem of entire functions.As an application we obtain a collection of extreme points for the class of normalized convex mappings.Our results extend both the rigidity of convex mappings and related extreme points from the unit ball to Reinhardt domains.