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.
Original language | English |
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Pages (from-to) | 581-593 |
Number of pages | 13 |
Journal | Journal of Geometric Analysis |
Volume | 13 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2003 |
Externally published | Yes |
Keywords
- Lucas polynomials
- Proper holomorphic mappings
- unit ball