A Convex Surface with Fractal Curvature

Abstract

We construct an example of a convex surface whose curvature is a fractal measure related to the Sierpinski Gasket. The construction produces the surface $S$ as a limit of convex polyhedra $P_n$. The curvature of each $P_n$ is a discrete measure supported on its vertices, and these discrete measures will converge to the fractal measure on $S$.

Samuel Wiese

PhD Student in Computer Science