A convex surface with fractal curvature
IANCU DIMA, RACHEL POPP, Robert S. Strichartz, Samuel C. Wiese · Digital Collections - Ithaca College Library (Ithaca College) · 2020
© 2020 World Scientific Publishing Company. We construct a surface that is obtained from the octahedron by pushing out four of the faces so that the curvature is supported in a copy of the Sierpinski gasket (SG) in each of them, and is essentially the self similar measure on SG. We then compute the bottom of the spectrum of the associated Laplacian using the finite element method on polyhedral approximations of our surface, and speculate on the behavior of the entire spectrum.