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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the topological extension to the boundary of biholomorphic maps in $ C\sp{n}$


Author: R. Michael Range
Journal: Trans. Amer. Math. Soc. 216 (1976), 203-216
MSC: Primary 32H99
MathSciNet review: 0387665
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Abstract: Let $ F:{D_1} \to {D_2}$ be a biholomorphic map between bounded domains in $ {{\mathbf{C}}^n}$ with piecewise smooth strictly pseudoconvex boundaries. It is shown that F is Hölder continuous of some positive order, and hence F extends to a homeomorphism of the closures of the domains. This generalizes recent results of G. M. Henkin and N. Vormoor for domains with smooth strictly pseudoconvex boundary.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0387665-9
PII: S 0002-9947(1976)0387665-9
Article copyright: © Copyright 1976 American Mathematical Society