Proper holomorphic mappings from the two-ball to the three-ball

Cima, J. A.; Suffridge, T. J.

doi:10.1090/S0002-9947-1989-0951881-4

Proper holomorphic mappings from the two-ball to the three-ball
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by J. A. Cima and T. J. Suffridge PDF

Trans. Amer. Math. Soc. 311 (1989), 227-239 Request permission

Abstract:

We prove that a proper mapping of the two ball in ${\mathbf {C}^{n}}$ into the three ball, which is ${C^2}$ on the closed two ball is equivalent to one of four normalized polynomial mappings. This improves the known result of Faran. The proof is basic using Taylor expansions.

References

H. Alexander, Proper holomorphic mappings in $C^{n}$, Indiana Univ. Math. J. 26 (1977), no. 1, 137–146. MR 422699, DOI 10.1512/iumj.1977.26.26010
J. A. Cima and T. J. Suffridge, A reflection principle with applications to proper holomorphic mappings, Math. Ann. 265 (1983), no. 4, 489–500. MR 721883, DOI 10.1007/BF01455949
James J. Faran, Maps from the two-ball to the three-ball, Invent. Math. 68 (1982), no. 3, 441–475. MR 669425, DOI 10.1007/BF01389412
James J. Faran, The linearity of proper holomorphic maps between balls in the low codimension case, J. Differential Geom. 24 (1986), no. 1, 15–17. MR 857373
S. M. Webster, On mapping an $n$-ball into an $(n+1)$-ball in complex spaces, Pacific J. Math. 81 (1979), no. 1, 267–272. MR 543749