Biholomorphic maps determined on the boundary
Annales de l'Institut Fourier, Volume 27 (1977) no. 3, p. 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:Df(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:Df(D) est biholomorphe.

@article{AIF_1977__27_3_129_0,
     author = {Mochizuki, Nozomu},
     title = {Biholomorphic maps determined on the boundary},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {27},
     number = {3},
     year = {1977},
     pages = {129-133},
     doi = {10.5802/aif.664},
     zbl = {0352.32016},
     mrnumber = {58 \#22681},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1977__27_3_129_0}
}
Mochizuki, Nozomu. Biholomorphic maps determined on the boundary. Annales de l'Institut Fourier, Volume 27 (1977) no. 3, pp. 129-133. doi : 10.5802/aif.664. http://www.numdam.org/item/AIF_1977__27_3_129_0/

[1] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, New Jersey, 1964. | MR 33 #1797 | Zbl 0129.13102