Abstract
The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials) achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products.
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Communicated by Steven Krantz
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D’Angelo, J.P., Kos, Š. & Riehl, E. A sharp bound for the degree of proper monomial mappings between balls. J Geom Anal 13, 581–593 (2003). https://doi.org/10.1007/BF02921879
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DOI: https://doi.org/10.1007/BF02921879