摘要
In this paper, we discuss the Lipschitz equivalence of self-similar sets with triangular pattern. This is a generalization of {1, 3, 5}-{1, 4, 5} problem proposed by David and Semmes. It is proved that if two such self-similar sets are totally disconnected, then they are Lipschitz equivalent if and only if they have the same Hausdorff dimension.
In this paper, we discuss the Lipschitz equivalence of self-similar sets with triangular pattern. This is a generalization of {1, 3, 5}-{1, 4, 5} problem proposed by David and Semmes. It is proved that if two such self-similar sets are totally disconnected, then they are Lipschitz equivalent if and only if they have the same Hausdorff dimension.
基金
supported by National Natural Science of China (Grant Nos. 11071224, 11071082, 11071090, 10671180, 10631040)
Natural Science Foundation of Ningbo (Grant No. 2009A610077)
the Fundamental Research Funds for the Central Universities, SCUT
the Science Foundation for the Youth of South China University of Technology (Grant No. E5090470)
