(A) study of M-invariant laplacian in $B_n$

Abstract

Let B$_n$ be the open unit ball of C$^n$, and let $\Delta$ be the ordinary Laplacian. Then it is easily proved that if f is a holomfunction in B$_n$ such that f(z)$\neq0$,for all z$\in$B$_n$ and $\Delta(\mid{f}\mid^p)=0$ on B$_n$, $-\infty<p<\infty$, then f must be constant. In this thesis, we prove an analogous result for the M-invariant Laplacian, $\Delta$, where M is the group of biholomorphic selfmaps of B$_n$.