Biholomorphic maps determined on the boundary

Mochizuki, Nozomu. "Biholomorphic maps determined on the boundary." Annales de l'institut Fourier 27.3 (1977): 129-133. <http://eudml.org/doc/74323>.

@article{Mochizuki1977,
abstract = {Let $D$ be a bounded domain in $\{\bf C\}^n$ such that the boundary $bD$ is topologically $S^\{2n-1\}$ in $\{\bf R\}^\{2n\}$ with a regular point; let $f:\widetilde\{D\}\rightarrow \{\bf C\}^n$ be a holomorphic map where $\widetilde\{D\}$ is a neighborhood of $\overline\{D\}$. If $f$ is one-to-one when restricted to $bD$, then $f:D\rightarrow f(D)$ is biholomorphic.},
author = {Mochizuki, Nozomu},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {129-133},
publisher = {Association des Annales de l'Institut Fourier},
title = {Biholomorphic maps determined on the boundary},
url = {http://eudml.org/doc/74323},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Mochizuki, Nozomu
TI - Biholomorphic maps determined on the boundary
JO - Annales de l'institut Fourier
PY - 1977
PB - Association des Annales de l'Institut Fourier
VL - 27
IS - 3
SP - 129
EP - 133
AB - Let $D$ be a bounded domain in ${\bf C}^n$ such that the boundary $bD$ is topologically $S^{2n-1}$ in ${\bf R}^{2n}$ with a regular point; let $f:\widetilde{D}\rightarrow {\bf C}^n$ be a holomorphic map where $\widetilde{D}$ is a neighborhood of $\overline{D}$. If $f$ is one-to-one when restricted to $bD$, then $f:D\rightarrow f(D)$ is biholomorphic.
LA - eng
UR - http://eudml.org/doc/74323
ER -