Non-degeneracy of the harmonic structure on Sierpinski Gaskets

Konstantinos Tsougkas

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arXiv · 1605.04117

Non-degeneracy of the harmonic structure on Sierpinski Gaskets

Konstantinos Tsougkas

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Abstract

We prove that the harmonic extension matrices for the level-k Sierpinski Gasket are invertible for every k>2. This has been previously conjectured to be true by Hino in [6] and [7] and tested numerically for k<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.

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BibTeX RIS

Konstantinos Tsougkas. 2017-05-31. Non-degeneracy of the harmonic structure on Sierpinski Gaskets. https://arxiv.org/abs/1605.04117

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