On the behavior of $1$-Laplacian Ratio Cuts on nearly rectangular domains

Wesley Hamilton, Jeremy L. Marzuola, Hau-tieng Wu

Given a connected set ${\Omega }_0\subset {\mathbb{R}}^2$, define a sequence of sets $({\Omega }_n{)}_{n=0}^{\infty }$ where ${\Omega }_{n+1}$ is the subset of ${\Omega }_n$ where the first eigenfunction of the (prop…