Dimension of pluriharmonic measure and polynomial endomorphisms of $\C^n$
Let $F$ be a polynomial endomorphism of $\C^n$ which extends holomorphically to $¶^n$. We prove that the dimension of $μ_F$, the pluriharmonic measure on the boundary of the filled Julia set of $F$, is bounded above by $2n-1$.
math.CV↗