A Convex Surface with Fractal Curvature


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 $S$.

A Convex Surface with Fractal Curvature, Fractals 28(4), 2020.
Samuel Wiese
Samuel Wiese
PhD Student in Computer Science