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Volume 36, Issue 4
The Non-Degeneracy of Harmonic Structures on Planar Sierpinski Gaskets

Shiping Cao & Hua Qiu

Anal. Theory Appl., 36 (2020), pp. 510-516.

Published online: 2020-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

We present a direct and short proof of the non-degeneracy of the harmonic structures on the level-$n$ Sierpinski gaskets for any $n\geq 2$, which was conjectured by Hino in [1,2] and confirmed to be true by Tsougkas [8] very recently using Tutte's spring theorem.

  • AMS Subject Headings

28A80

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COPYRIGHT: © Global Science Press

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@Article{ATA-36-510, author = {Cao , Shiping and Qiu , Hua}, title = {The Non-Degeneracy of Harmonic Structures on Planar Sierpinski Gaskets}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {36}, number = {4}, pages = {510--516}, abstract = {

We present a direct and short proof of the non-degeneracy of the harmonic structures on the level-$n$ Sierpinski gaskets for any $n\geq 2$, which was conjectured by Hino in [1,2] and confirmed to be true by Tsougkas [8] very recently using Tutte's spring theorem.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-SU6}, url = {http://global-sci.org/intro/article_detail/ata/18467.html} }
TY - JOUR T1 - The Non-Degeneracy of Harmonic Structures on Planar Sierpinski Gaskets AU - Cao , Shiping AU - Qiu , Hua JO - Analysis in Theory and Applications VL - 4 SP - 510 EP - 516 PY - 2020 DA - 2020/12 SN - 36 DO - http://doi.org/10.4208/ata.OA-SU6 UR - https://global-sci.org/intro/article_detail/ata/18467.html KW - Fractal analysis, harmonic functions, fractal Laplacians, harmonic structures, Sierpinski gaskets. AB -

We present a direct and short proof of the non-degeneracy of the harmonic structures on the level-$n$ Sierpinski gaskets for any $n\geq 2$, which was conjectured by Hino in [1,2] and confirmed to be true by Tsougkas [8] very recently using Tutte's spring theorem.

Cao , Shiping and Qiu , Hua. (2020). The Non-Degeneracy of Harmonic Structures on Planar Sierpinski Gaskets. Analysis in Theory and Applications. 36 (4). 510-516. doi:10.4208/ata.OA-SU6
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