46 citations · 191 across the 47 of their papers we have counts for
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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…
A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket
Shiping Cao, Shuangping Li, Robert S. Strichartz +1
We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special…
The Mathieu Differential Equation and Generalizations to Infinite Fractafolds
Shiping Cao, Anthony Coniglio, Xueyan Niu +2
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by c…
Spectral Properties of Laplacians on Snowflake domains and filled Julia sets
Robert S. Strichartz, Samuel C. Wiese
We present eigenvalue data and pictures of eigenfunctions of the classic and quadratic snowflake fractal and of quadratic filled Julia sets. Furthermore, we approximate the area an…
Geometry and Laplacian on Discrete Magic Carpets
Eric Goodman, Chun-Yin Siu, Robert S. Strichartz
We study several variants of the classical Sierpinski Carpet (SC) fractal. The main examples we call infinite magic carpets (IMC), obtained by taking an infinite blowup of a discre…