3 papers
math.AP2019
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…
math.AP2019
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…
math.AP2018
Spectrum of the Laplacian on Regular Polyhedra
Evan Greif, Daniel Kaplan, Robert S. Strichartz +1
We study eigenvalues and eigenfunctions of the Laplacian on the surfaces of four of the regular polyhedrons: tetrahedron, octahedron, icosahedron and cube. We show two types of eig…