本项目的研究内容主要涉及到分形集的拟对称极小性，分形集上拟对称映射的等价刻画以及用加倍测度对分形集进行分类等问题，它们是分形几何、几何测度论与拟对称映射交叉领域中重要且相当具有难度的问题，有理论及应用双重重要意义。我们准备做：1）考察分形集的拟对称极小性（特别是packing极小性）: 从简单的一维分形集出发，进一步系统深入地研究一些更复杂或高维的集合，找出一些重要且特殊的拟对称极小集，进而研究拟对称映射对分形集分形维数的改变情况。2）对分形集上的拟对称映射做一些等价刻画:从简单的一维分形集出发，研究更复杂的欧氏空间和一般度量空间上的分形集，对这些分形集上的拟对称映射做等价刻画。3）利用加倍测度对分形集进行分类: 从简单的一、二维分形集出发，研究更复杂的分形集，用加倍测度将它们进行细致的分类。我们将综合运用所掌握的数学工具，努力发掘新思想，力争圆满回答这些问题。

The research of our work are mainly related to the quasisymmetric minimality for fractal sets, the equivalent conditions of quasisymmetric mappings on fractal sets, the classifications of fractal sets with doubling measures. They are important and difficult topics in the crossroads between fractal geometry, geometric measure theory and quasisymmetric mapping, they are with the theory and application of dual significance. We will do some research below: 1) Studing the quasisymmetric minimality (especially packing minimality) for fractal sets: we will start the studing from the one-dimensional fractal sets, then study some more complicated and higher dimension sets and find out some special and improtant quasisymmetric minimal sets. Morever we will study about the quasisymmetric mappings how to influence the fractal dimensions for fractal sets. 2) Doing some equivalent characterizations for the fractal set: we will start the studing from the one-dimensional fractal sets, then study some more complicated fractal sets on Euclid and general metric space to give some equivalent conditions to the quasisymmetric mappings of these sets. 3) Classifying the fractal sets by doubling measures: we will start the studing from the one or two-dimensional fractal sets, then study some more complicated sets to do some more accurate classification to them by doubling measures. We will effectively use our mathematical tools and find new ideas, and try to answer these questions satisfactorily.