Volume 28, Issue 3
Mihai Cucuringu and Robert S. Strichartz (2008). Infinitesimal resistance metrics on Sierpinski gasket type fractals. Analysis: Vol. 28, Issue 3, pp. 319-331.
doi: 10.1524/anly.2008.0917

Infinitesimal resistance metrics on Sierpinski gasket type fractals

Mihai Cucuringu und Robert S. Strichartz

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Keywords: Sierpinski gasket, analysis on fractals, effective resistance metric



We prove the existence of an infinitesimal resistance metric on the Sierpinski gasket (SG) at boundary points, junction points and periodic points. This is a renormalized limit of the effective resistance metric as we zoom in on the point, and satisfies a self-similar identity. We obtain similar results on PCF fractals with three boundary points.