A sharp bound for the degree of proper monomial mappings between balls (Q1429297)

In this interesting paper the authors prove the following theorem. Suppose that \(p\) is a polynomial in two real variables \((x,y)\) with real coefficients, such that \(p(x,y)=1\), if \(x+y=1\). Let \(N\) be the number of distinct monomials in \(p\), and let \(d\) be the degree of \(p\). Then \(d\leq 2N-3\) and this result is sharp. As a corollary, they show that if \(f\) is a proper holomorphic monomial mapping from the unit ball in \(\mathbb C^2\) to the unit ball in \(\mathbb C^N\), then the degree of \(f\) does not exceed \(2N-3\), and this result is sharp.