A definitive determinant majorization result for nonlinear operators

Let g be a Gårding–Dirichlet operator on the set S(n) of symmetric n×n matrices. We assume that g is I-central, that is, DIg=kI for some k>0. Then g (A)1 N≥g(I)1 N(detA)1 n∀A>0. From work of Guo, Phong, Tong, Abja, Dinew, Olive, and many others, this inequality has important applications.