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<p>In this paper, we consider a Generalized Bernstein Theorem for a type of generalized minimal surfaces, namely minimal Plateau surfaces. We show that if a complete orientable minimal Plateau surface is stable and has quadratic area growth in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10455_2025_10002_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^3 \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>, then it must be flat.</p>

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Generalized Bernstein Theorem for stable minimal plateau surfaces

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • Gaoming Wang

摘要

In this paper, we consider a Generalized Bernstein Theorem for a type of generalized minimal surfaces, namely minimal Plateau surfaces. We show that if a complete orientable minimal Plateau surface is stable and has quadratic area growth in \(\mathbb {R}^3 \) R 3 , then it must be flat.