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<p>In this article, we show the existence and uniqueness of a family of complete elliptic Weingarten surfaces of minimal type, which are invariant by a uniparametric group of horizontal translation. Moreover, we give a complete description of the generating curve of each of these surfaces when the elliptic function satisfies <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(f(x)&gt;0\)</EquationSource> </InlineEquation> for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(x\ne 0\)</EquationSource> </InlineEquation>.</p>

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Elliptic Weingarten surfaces of minimal type invariant by left translations in \(\textrm{Sol}_3\)

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Albetã C. Mafra,
  • Carlos Peñafiel,
  • Erick J. Palacios Escobar

摘要

In this article, we show the existence and uniqueness of a family of complete elliptic Weingarten surfaces of minimal type, which are invariant by a uniparametric group of horizontal translation. Moreover, we give a complete description of the generating curve of each of these surfaces when the elliptic function satisfies \(f(x)>0\) for \(x\ne 0\) .