# Biholomorphic maps determined on the boundary

Annales de l'institut Fourier (1977)

- Volume: 27, Issue: 3, page 129-133
- ISSN: 0373-0956

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topMochizuki, 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 -

## References

top- [1] S. STERNBERG, Lectures on Differential Geometry, Prentice-Hall, New Jersey, 1964. Zbl0129.13102MR33 #1797

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