本项目的研究内容主要涉及分形集的拟对称极小性及分形集上拟对称映射的等价刻画，涉及到分形几何，几何测度论，拟共形映射等问题，它们是分形几何与拟对称映射交叉领域中重要并且相当具有难度的问题，也是国内外同行所关注的研究热点。1）我们将分类、系统深入地研究分形集关于packing维数的拟对称极小性：我们将从一维Moran集出发，进而研究一些更复杂的分形集，找出一些特殊的拟对称packing极小集。2）我们将对分形集上的拟对称映射做一些等价刻画：我们将从欧氏空间上的分形集出发，进而研究一般度量空间上的分形集，对这些集合上的拟对称映射做等价刻画。本项目研究的问题相对独立但密切相关，具有理论及应用双重重要意义。

The research of our work are mainly related to quasisymmetric minimality for fractal sets and equivalent conditions of quasisymmetric mappings for fractal sets，they are important and difficult topics in crossroads between fractal geometry and quasisymmetric mapping, they are also hotspot topics for the domestic and foreign counterparts to research. 1) We will study quasisymmetric minimality on packing dimension for fractal sets: we will start the studing from the one-dimensional Moran set, then study some more complicated fractal sets and.find out some special quasisymmetric packing minimal sets. 2) We will do some equivalent characterizations of the one-dimensional fractal sets: we will start the studing from fractal sets on Euclid space, and then study fractal sets on general space, and give some equivalent conditions to the quasisymmetric mappings of these sets. These questions are relatively independent but closely related, with the theory and application of dual significance.