  Given a compact Alexadrov $n$-space $Z$ with curvature curv $\ge \kappa$, and
let $f: Z\to X$ be a distance non-increasing onto map to another Alexandrov
$n$-space with curv $\ge \kappa$. The relative volume rigidity conjecture says
that if $X$ achieves the relative maximal volume i.e. $vol(Z)=vol(X)$, then $X$
is isometric to $Z/\sim$, where $z, z'\in\partial Z$ and $z\sim z'$ if only if
$f(z)=f(z')$. We will partially verify this conjecture, and give a
classification for compact Alexandrov $n$-spaces with relatively maximal
volume. We will also give an elementary proof for a pointed version of
Bishop-Gromov relative volume comparison with rigidity in Alexandrov geometry.
