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<p>We study framed surfaces, which are a class of Euclidean minimal and hyperbolic CMC-1 surfaces that generalize immersed minimal surfaces in <InlineEquation ID="IEq1"> <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> and Bryant surfaces. For this class we prove a lower bound on the (unrestricted) Morse index by a linear function of the genus, number of ends and number of branch points (counting multiplicity), generalizing a result by Chodosh and the first author (J Differ Geom 123(3):431–459, 2023). We include as well a description of the 1-to-1 correspondence between Euclidean minimal and Bryant surfaces, known in the literature as <i>Lawson’s correspondence</i>.</p>

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On the topology and index of minimal and Bryant framed surfaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月21日

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  • Davi Maximo,
  • Franco Vargas Pallete

摘要

We study framed surfaces, which are a class of Euclidean minimal and hyperbolic CMC-1 surfaces that generalize immersed minimal surfaces in \(\mathbb {R}^3\) R 3 and Bryant surfaces. For this class we prove a lower bound on the (unrestricted) Morse index by a linear function of the genus, number of ends and number of branch points (counting multiplicity), generalizing a result by Chodosh and the first author (J Differ Geom 123(3):431–459, 2023). We include as well a description of the 1-to-1 correspondence between Euclidean minimal and Bryant surfaces, known in the literature as Lawson’s correspondence.