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<p>The main goal of this work is to prove an instance of the unique continuation principle for area minimizing integral currents. More precisely, we consider an <i>m</i>-dimensional area minimizing integral current and an <i>m</i>-dimensional minimal surface, both contained in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {R}}^{n+m}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mi>m</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n\ge 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. We show that if, in an integral sense, the current has an infinite order of contact with the minimal surface at a point, then the current and the minimal surface coincide in a neighbourhood of that point.</p>

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Unique Continuation for Area Minimizing Currents

  • 期刊论文

  • 发表日期：

    2026年5月24日

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  • Camillo Brena,
  • Stefano Decio

摘要

The main goal of this work is to prove an instance of the unique continuation principle for area minimizing integral currents. More precisely, we consider an m-dimensional area minimizing integral current and an m-dimensional minimal surface, both contained in \({\mathbb {R}}^{n+m}\) R n + m with \(n\ge 1\) n ≥ 1 . We show that if, in an integral sense, the current has an infinite order of contact with the minimal surface at a point, then the current and the minimal surface coincide in a neighbourhood of that point.