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arXiv · 2501.14299

Removable singularities for nonlocal minimal graphs

Minhyun Kim
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Abstract

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

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Minhyun Kim. 2026-01-30. Removable singularities for nonlocal minimal graphs. https://doi.org/10.1007/s12220-026-02344-w

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