Gaps in the spectrum of the Laplacian on $3N$-Gaskets
Gaps in the spectrum of the Laplacian on $3N$-Gaskets
This article develops analysis on fractal $3N$-gaskets, a class of post-critically finite fractals which include the Sierpinski triangle for $N=1$, specifically properties of the Laplacian $\Delta$ on these gaskets. We first prove the existence of a self-similar geodesic metric on these gaskets, and prove heat kernel estimates for this Laplacian …