Let $X$ be the interior of a compact manifold $\overline{X}$ of dimension $n+1$ with boundary $M=\partial X$, and $g_{+}$ be a conformally compact metric on $X$, namely $\overline{g}\equiv r^2{g}_{+}$ extends continuously (or with some degree of smoothness) as a metric to $X$, where $r$ denotes a defining function for $M$, i.e. $r>0$ on $X$ and $r=0$, $dr\ne 0$ on $M$. The restrction of $\overline{g}$ to $TM$ rescales upon changing $r$, so defines invariantly a conformal class of metrics on $M$, which is called the conformal infinity of $g_{+}$. In the present paper, the author considers conformally compact metrics...