Rigidity for convex mappings of Reinhardt domains and its applications
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In this paper, we investigate rigidity and its application 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 Kobayashi metric and 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.
Keywordsconvex mapping Reinhardt domain scaling method Kobayashi metric extreme point
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This work was supported by National Natural Science Foundation of China (Grant Nos. 11471111, 11571105 and 11671362) and the Natural Science Foundation of Zhejiang Province (Grant No. LY16A010004). The authors are grateful to the anonymous referees for their careful reading of the manuscript and many helpful suggestions.
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