  In \cite{ZW}, the notion of homogenous perfect set as a generalization of
Cantor type sets is introduced. Their Hausdorff, lower box-counting, upper
box-counting and packing dimensions are studied in \cite{ZW} and \cite{WW}. In
this paper, we show that the homogenous perfect set be minimal for
1-dimensional quasisymmetric maps, which generalize the conclusion in \cite{MS}
about the uniform Cantor cantor set to the homogenous perfect set.
