A new gap phenomenon for proper holomorphic mappings from ${\BB}^n$ into ${\BB}^{N}$

On holomorphic automorphisms of a class of non-homogeneous rigid hypersurfaces in ℂ N+1

“…Huang, Ji and Xu classified the proper holomorphic mappings f : B n → B N between the unit balls in C n and C N with N ≥ n ≥ 1 (cf. [10,11]). …”

The classification of proper holomorphic mappings between special Hartogs triangles of different dimensions

“…For n > 2, the authors of [2] proved that there are only two equivalence classes in Rat(B n , B N ). In [3], the authors got a new gap phenomenon for proper holomorphic mappings from B n to B N when N ≤ 3n − 4. When N < 2n − 1 Huang Xiaojun gave the following classical theorem on the classification of proper holomorphic mappings from B n to B N .…”

“…The classification of proper holomorphic mappings (see the definition in [1]) is an important and difficult problem, especially between bounded domains of different dimensions (see [2][3][4]). Assume that g, f : D 1 → D 2 are proper holomorphic mappings, D 1 and D 2 are bounded domains in C n and C N respectively.…”

“…Proper holomorphic mapping theory dates from 1950s, and there are many good results on it (see [1][2][3][4][5][6][7][8][9]). The classification of proper holomorphic mappings (see the definition in [1]) is an important and difficult problem, especially between bounded domains of different dimensions (see [2][3][4]).…”

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“…Making use of results obtained in the previous work [1,2] , we give a complete description for the modular space for maps in Rat(B 2 , B N ) with degree 2 under the above mentioned equivalence relation. Our main result is the following Theorem 1.1.…”