A sharp bound for the degree of proper monomial mappings between balls

• DOI: 10.1007/bf02921879
• Publication Date: 2011-12-09T19:54:41Z
• Authors: John P. D’Angelo; Šimon Kos; Emily Riehl
• Keywords: Ball (mathematics); Degree (music)

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.