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<p>We prove the removable singularity theorem for nonlocal minimal graphs. Specifically, we show that any nonlocal minimal graph in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \setminus K\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo lspace="0.15em" rspace="0.15em" stretchy="false">\</mo> <mi>K</mi> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Omega \subset \mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> is an open set and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(K \subset \Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>⊂</mo> <mi mathvariant="normal">Ω</mi> </mrow> </math></EquationSource> </InlineEquation> is a compact set of (<i>s</i>,&#xa0;1)-capacity zero, is indeed a nonlocal minimal graph in all of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>.</p>

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Removable Singularities for Nonlocal Minimal Graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月30日

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  • Minhyun Kim

摘要

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