A symmetrization inequality for plurisubharmonic functions (Q1318055)

Let \(u\) be a complex-homogeneous plurisubharmonic function on \(\mathbb{C}^ n\), and let \(E_ 1,\dots,E_ n\) be nonempty subsets of \(\mathbb{C}\). Then \[ \sup u(E_ 1, \dots,E_ n) \geq \sup u(D_ 1,\dots,D_ n), \] where \(D_ j\) is the closed disc in \(\mathbb{C}\) with centre 0 and the same capacity as \(E_ j\). This result has applications to capacity and to the growth of plurisubharmonic functions of finite order.