We introduce a graph-directed pair of planar self-similar sets that possess fully symmetric Laplacians. For these two fractals, due to Shima’s celebrated criterion, we point out that one admits the spectral decimatio...We introduce a graph-directed pair of planar self-similar sets that possess fully symmetric Laplacians. For these two fractals, due to Shima’s celebrated criterion, we point out that one admits the spectral decimation by the canonic graph approximation and the other does not. For the second fractal, we adjust to choosing a new graph approximation guided by the directed graph, which still admits spectral decimation. Then we make a full description of the Dirichlet and Neumann eigenvalues and eigenfunctions of both of these two fractals.展开更多
We present a direct and short proof of the non-degeneracy of the harmonic structures on the level-n Sierpinski gaskets for any n≥2,which was conjectured by Hino in[1,2]and confirmed to be true by Tsougkas[8]very rece...We present a direct and short proof of the non-degeneracy of the harmonic structures on the level-n Sierpinski gaskets for any n≥2,which was conjectured by Hino in[1,2]and confirmed to be true by Tsougkas[8]very recently using Tutte’s spring theorem.展开更多
基金supported by National Natural Science Foundation of China(Grant No.12071213)the Natural Science Foundation of Jiangsu Province in China(Grant No.BK20211142)。
文摘We introduce a graph-directed pair of planar self-similar sets that possess fully symmetric Laplacians. For these two fractals, due to Shima’s celebrated criterion, we point out that one admits the spectral decimation by the canonic graph approximation and the other does not. For the second fractal, we adjust to choosing a new graph approximation guided by the directed graph, which still admits spectral decimation. Then we make a full description of the Dirichlet and Neumann eigenvalues and eigenfunctions of both of these two fractals.
基金the Nature Science Foundation of China,Grant No.12071213.
文摘We present a direct and short proof of the non-degeneracy of the harmonic structures on the level-n Sierpinski gaskets for any n≥2,which was conjectured by Hino in[1,2]and confirmed to be true by Tsougkas[8]very recently using Tutte’s spring theorem.
