On the Łojasiewicz exponent of the gradient of a polynomial function

Let ${\displaystyle h=\sum h_{\alpha \beta }{X}^{\alpha }{Y}^{\beta }}$ be a polynomial with complex coefficients. The Łojasiewicz exponent of the gradient of h at infinity is the least upper bound of the set of all real λ such that ${\displaystyle |\nabla h(x,y)|\ge c{\left|\begin{array}{cc}x& y\end{array}\right|}^{\lambda }}$ in a neighbourhood of infinity in ℂ², for c > 0. We estimate this quantity in terms of the Newton diagram of h. Equality is obtained in the nondegenerate case.