On the topological extension to the boundary of biholomorphic maps in 𝐶ⁿ

Range, R. Michael

doi:10.1090/S0002-9947-1976-0387665-9

On the topological extension to the boundary of biholomorphic maps in $C^{n}$
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by R. Michael Range PDF

Trans. Amer. Math. Soc. 216 (1976), 203-216 Request permission

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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