46 citations · 191 across the 47 of their papers we have counts for
51 papers
Eigenvalues of Laplacians on Higher Dimensional Vicsek Set Graphs
Shiping Cao, Robert S. Strichartz, Melissa Wei
We study the graphs associated with Vicsek sets in higher dimensional settings. First, we study the eigenvalues of the Laplacians on the approximating graphs of the Vicsek sets, fi…
Sobolev Orthogonal Polynomials on the Sierpinski Gasket
Qingxuan Jiang, Tian Lan, Kasso Okoudjou +4
We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket (). These orthogonal polynomials arise through the Gram-Schmidt orthogonalisation process applied…
Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps
Shiping Cao, Malte S. Hassler, Hua Qiu +2
We study the balanced resistance forms on the Julia sets of Misiurewicz-Sierpinski maps, which are self-similar resistance forms with equal weights. In particular, we use a theorem…
Laplacians on Julia sets of rational maps
Malte S. Hassler, Hua Qiu, Robert S. Strichartz
The study of Julia sets gives a new and natural way to look at fractals. When mathematicians investigated the special class of Misiurewicz's rational maps, they found out that ther…
Spectral analysis beyond on Sierpinski lattices
Shiping Cao, Yiqi Huang, Hua Qiu +2
We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of , remains the same for any …
A Convex Surface with Fractal Curvature
Iancu Dima, Rachel Popp, Robert S. Strichartz +1
We construct a surface that is obtained from the octahedron by pushing out 4 of the faces so that the curvature is supported in a copy of the Sierpinski gasket in each of them, and…