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<p>In this article, we study the isoperimetric problem in the Teichmüller-Randers metric that interpolates between Thurston’s asymmetric metric and the Teichmüller metric (which coincides with the hyperbolic metric) on the Teichmüller space of the torus. We also investigate some geometric properties of the Teichmüller-Randers space. More precisely, we explicitly compute the <i>S</i>-curvature, Riemann curvature, Ricci curvature, flag curvature, and Zermelo navigation data for this Teichmüller-Randers metric.</p>

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The Isoperimetric Problem in the Teichmüller Space of Torus

  • 期刊论文

  • 发表日期：

    2026年5月16日

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  • Arti Sahu Gangopadhyay,
  • Krishnendu Gongopadhyay,
  • Bankteshwar Tiwari

摘要

In this article, we study the isoperimetric problem in the Teichmüller-Randers metric that interpolates between Thurston’s asymmetric metric and the Teichmüller metric (which coincides with the hyperbolic metric) on the Teichmüller space of the torus. We also investigate some geometric properties of the Teichmüller-Randers space. More precisely, we explicitly compute the S-curvature, Riemann curvature, Ricci curvature, flag curvature, and Zermelo navigation data for this Teichmüller-Randers metric.