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<p>We prove a Hölder-type inequality (in the spirit of Joksimović and Seyfaddini in Int Math Res Not IMRN 8:6303–6324, 2024) for the Hausdorff distance between Lagrangians with respect to the Lagrangian spectral distance or the Hofer–Chekanov distance. This inequality is established via methods developed by the first author (Chassé in Int J Math 34(5):2350024, 2023; Chassé in Differ Geom Appl 94:Paper No. 102123, 22, 2024) to understand the symplectic geometry of certain collections of Lagrangians under metric constraints.</p>

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A Hölder-type inequality for the Hausdorff distance between Lagrangians

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月20日

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  • Jean-Philippe Chassé,
  • Rémi Leclercq

摘要

We prove a Hölder-type inequality (in the spirit of Joksimović and Seyfaddini in Int Math Res Not IMRN 8:6303–6324, 2024) for the Hausdorff distance between Lagrangians with respect to the Lagrangian spectral distance or the Hofer–Chekanov distance. This inequality is established via methods developed by the first author (Chassé in Int J Math 34(5):2350024, 2023; Chassé in Differ Geom Appl 94:Paper No. 102123, 22, 2024) to understand the symplectic geometry of certain collections of Lagrangians under metric constraints.