Percolation on the Non-p.c.f. Sierpiński Gasket and Hexacarpet

Analysis on Products of Fractals

For a class of post–critically finite (p.c.f.) fractals, which includes the Sierpinski gasket (SG), there is a satisfactory theory of analysis due to Kigami, including energy, harmonic functions and Laplacians. In particular, the Laplacian coincides with the generator of a stochastic process constructed independently by probabilistic methods. The probabilistic method is also available for non–p...

Energy and Laplacian on the Sierpiński Gasket

This is an expository paper which includes several topics related to the Dirichlet form analysis on the Sierpiński gasket. We discuss the analog of the classical Laplacian; approximation by harmonic functions that gives a notion of a gradient; directional energies and an equipartition of energy; analysis with respect to the energy measure; harmonic coordinates; and non self-similar Dirichlet fo...

Multiple solutions for a class of nonlinear elliptic equations on the Sierpiński gasket

Coloring Sierpiński graphs and Sierpiński gasket graphs

Sierpiński graphs S(n, 3) are the graphs of the Tower of Hanoi with n disks, while Sierpiński gasket graphs Sn are the graphs naturally defined by the finite number of iterations that lead to the Sierpiński gasket. An explicit labeling of the vertices of Sn is introduced. It is proved that Sn is uniquely 3-colorable, that S(n, 3) is uniquely 3-edgecolorable, and that χ′(Sn) = 4, thus answering ...

Some Spectral Properties of Pseudo-differential Operators on the Sierpiński Gasket

We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Our results used in a fundamental way the existence of localized eigenfunctions for the Laplacian on this fractal.