no. 3
Biholomorphic maps determined on the boundary
Annales de l'Institut Fourier, Tome 27 (1977) no. 3, pp. 129-133

Let D be a bounded domain in C n such that the boundary bD is topologically S 2n-1 in R 2n with a regular point; let f:D ˜→C n be a holomorphic map where D ˜ is a neighborhood of D ¯. If f is one-to-one when restricted to bD, then f:D→f(D) is biholomorphic.

Soit D un domaine borné de C n tel que la frontière bD soit topologiquement égale à S 2n-1 dans R 2n contenant un point régulier ; soit f:D ˜→C n une application holomorphe où D ˜ est un voisinage de D ¯. Si f|bD est biunivoque f:D→f(D) est biholomorphe.

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     author = {Mochizuki, Nozomu},
     title = {Biholomorphic maps determined on the boundary},
     journal = {Annales de l'Institut Fourier},
     pages = {129--133},
     year = {1977},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {27},
     number = {3},
     doi = {10.5802/aif.664},
     mrnumber = {58 #22681},
     zbl = {0352.32016},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.664/}
}
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Mochizuki, Nozomu. Biholomorphic maps determined on the boundary. Annales de l'Institut Fourier, Tome 27 (1977) no. 3, pp. 129-133. doi: 10.5802/aif.664

[1] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, New Jersey, 1964. | Zbl | MR

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