Journal of Fractal Geometry
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Published online: 2019-03-21
Non-degeneracy of the harmonic structure on Sierpiński gasketsKonstantinos Tsougkas (1) Uppsala University, Sweden
We prove that the harmonic extension matrices for the two dimensional level-$k$ Sierpiński gasket are invertible for every $k \geq 2$. This has been previously conjectured to be true by Hino in  and  and tested numerically for $k \leq 50$. We also give a necessary condition for the non-degeneracy of the harmonic structure for general finitely ramified self-similar sets based on the vertex connectivity of their first graph approximation.
Keywords: Harmonic structure, harmonic extension matrices, energy Laplacian, Sierpiński gasket, prefractal graphs
Tsougkas Konstantinos: Non-degeneracy of the harmonic structure on Sierpiński gaskets. J. Fractal Geom. 6 (2019), 143-156. doi: 10.4171/JFG/73