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Abstract <p> In this article, we use the inverse function theorem for Banach spaces to interpolate a given real analytic spacelike curve <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1172_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(a\)</EquationSource> </InlineEquation> in the Lorentz–Minkowski space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1172_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{L}^3\)</EquationSource> </InlineEquation> to another real analytic spacelike curve <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1172_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(c\)</EquationSource> </InlineEquation>, which is “close” enough to <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1172_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(a\)</EquationSource> </InlineEquation> in a certain sense, by constructing a maximal surface containing them. Throughout this study, the Björling problem and Schwarz’s solution to it play pivotal roles. </p>

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Interpolation by Maximal Surfaces

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Rukmini Dey,
  • Rahul Kumar Singh

摘要

Abstract

In this article, we use the inverse function theorem for Banach spaces to interpolate a given real analytic spacelike curve \(a\) in the Lorentz–Minkowski space \(\mathbb{L}^3\) to another real analytic spacelike curve \(c\) , which is “close” enough to \(a\) in a certain sense, by constructing a maximal surface containing them. Throughout this study, the Björling problem and Schwarz’s solution to it play pivotal roles.