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<p>In this paper, we study strongly fillable curves in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\partial _{\infty }\left( \mathbb {H} ^2\times \mathbb {R} \right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>∂</mi> <mi>∞</mi> </msub> <mfenced close=")" open="("> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mn>2</mn> </msup> <mo>×</mo> <mi mathvariant="double-struck">R</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, establishing one existence result and one nonexistence result. In particular, by replacing Scherk barriers with newly constructed barriers, we eliminate the regularity condition previously imposed on the infinite curves in Coskunuzer’s main theorem [<CitationRef CitationID="CR5">5</CitationRef>].</p>

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Asymptotic Plateau Problem in \(\mathbb {H} ^2\times \mathbb {R}\): Strongly Fillable Curves

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Shuangqi Liu,
  • Shengliang Pan

摘要

In this paper, we study strongly fillable curves in \(\partial _{\infty }\left( \mathbb {H} ^2\times \mathbb {R} \right) \) ∂ ∞ H 2 × R , establishing one existence result and one nonexistence result. In particular, by replacing Scherk barriers with newly constructed barriers, we eliminate the regularity condition previously imposed on the infinite curves in Coskunuzer’s main theorem [5].