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Let F be a proper rational map from the complex ball Bn into BN with n>7 and 3n+1  N 4n-7. Then F is equivalent to a map (G, 0,... 0) where G is a proper holomorphic map from Bn into B3n. ? 2013 Springer-Verlag Berlin Heidelberg.

On the third gap for proper holomorphic maps between balls