The Non-Degeneracy of Harmonic Structures on Planar Sierpinski Gaskets

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.