A Convex Surface with Fractal Curvature
Analysis of PDEs
2020-07-15 v1
Abstract
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 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.
Cite
@article{arxiv.1907.06265,
title = {A Convex Surface with Fractal Curvature},
author = {Iancu Dima and Rachel Popp and Robert S. Strichartz and Samuel C. Wiese},
journal= {arXiv preprint arXiv:1907.06265},
year = {2020}
}
Comments
18 pages, 24 pictures