English

Removable singularities for nonlocal minimal graphs

Differential Geometry 2026-02-03 v2 Analysis of PDEs

Abstract

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

Keywords

Cite

@article{arxiv.2501.14299,
  title  = {Removable singularities for nonlocal minimal graphs},
  author = {Minhyun Kim},
  journal= {arXiv preprint arXiv:2501.14299},
  year   = {2026}
}

Comments

16 pages

R2 v1 2026-06-28T21:15:51.660Z