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<p>In this paper, we give a slight improvement of El Soufi–Ilias–Ros’s upper bound of the first Laplace eigenvalue on a torus in a fixed conformal class. We also optimize Montiel–Ros’s argument to obtain a better upper bound of the conformal area for certain rectangular tori.</p>

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An Upper Bound for the First Eigenvalue of Laplacian on Tori

  • 期刊论文

  • 发表日期：

    2025年11月9日

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  • Fan Kang,
  • Zhenlei Zhang

摘要

In this paper, we give a slight improvement of El Soufi–Ilias–Ros’s upper bound of the first Laplace eigenvalue on a torus in a fixed conformal class. We also optimize Montiel–Ros’s argument to obtain a better upper bound of the conformal area for certain rectangular tori.