Removable singularities for nonlocal minimal graphs

Abstract

We prove the removable singularity theorem for nonlocal minimal graphs. Specifically, we show that any nonlocal minimal graph in $\hat{I}\text{c◯}\setminus K$, where $\hat{I}\text{c◯}\subset {\mathbb{R}}^n$ is an open set and $K\subset \hat{I}\text{c◯}$ is a compact set of $(s,1)$-capacity zero, is indeed a nonlocal minimal graph in all of $\hat{I}\text{c◯}$.

16 pages