This research demonstrates the applicability of removable singularity theorem in nonlocal minimal graphs, suggesting their completeness in open sets.
We prove the removable singularity theorem for nonlocal minimal graphs. Specifically, we show that any nonlocal minimal graph in Ω K Ω \ K , where Ω ⊂ Rⁿ Ω ⊂ R n is an open set and K ⊂ Ω K ⊂ Ω is a compact set of ( s , 1)-capacity zero, is indeed a nonlocal minimal graph in all of Ω Ω .
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Minhyun Kim (2026) studied this question.
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