A sharp bound for the degree of proper monomial mappings between balls |
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Authors: | John P D’Angelo ?imon Kos Emily Riehl |
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Institution: | (1) Department of Mathematics, University of Illinois, 1409 W. Green St., 61801 Urbana, IL;(2) Center for Nonlinear Studies, Los Alamos National Laboratory, MS B258, 87545 Los Alamos, NM |
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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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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 32B99 32H02 11B309 |
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