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<p>In this paper, we consider a variational problem describing a soap film confined to a cylindrical tube, which was proposed by Cox and Jones (J Eng Math 86:1–7, 2014). Particularly we are interested in the stability and the instability of helical surfaces, which are critical points of the associated energy functional. Seguin and Fried (Calc Var PDEs 54:969–988, 2015) derived an eigenvalue problem which is equivalent to the second variation stability criterion and obtained results regarding the stability of helical surfaces. By evaluating the minimum eigenvalue carefully, we establish the instability result of twisted helical surfaces. We also improve the previous result on the stability of helical surfaces.</p>

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Stability analysis of helical soap films for the Plateau problem confined to a cylindrical tube

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Atsuki Fujita,
  • Tatsuya Watanabe

摘要

In this paper, we consider a variational problem describing a soap film confined to a cylindrical tube, which was proposed by Cox and Jones (J Eng Math 86:1–7, 2014). Particularly we are interested in the stability and the instability of helical surfaces, which are critical points of the associated energy functional. Seguin and Fried (Calc Var PDEs 54:969–988, 2015) derived an eigenvalue problem which is equivalent to the second variation stability criterion and obtained results regarding the stability of helical surfaces. By evaluating the minimum eigenvalue carefully, we establish the instability result of twisted helical surfaces. We also improve the previous result on the stability of helical surfaces.