一类齐次完全集的拟对称极小性

The quasisymmetric minimality of a class of homogeneous perfect sets

研究齐次完全集的拟对称极小性.利用质量分布原理,证明了一类特殊的Hausdorff维数为1的齐次完全集是拟对称Hausdorff极小集.还证明了类似结论对packing维数也成立.

In this paper we study quasisymmetric minimality of homogeneous perfect sets. By using principle of mass distribution, we prove that a class of homogeneous perfect sets of Hausdorff dimension 1 is quasisymmetrically Hausdorff minimal. A similar result for quasisymmetrically packing minimality is also obtained.