A Hölder-type inequality for the Hausdorff distance between Lagrangians

2023/08/31 by Chassé, Jean-Philippe, Leclercq, Rémi
#53C17 #53D12 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2308.16695

Abstract

We prove a Hölder-type inequality for the Hausdorff distance between Lagrangians with respect to the Lagrangian spectral distance or the Hofer-Chekanov distance in the spirit of Joksimović-Seyfaddini [arXiv:2207.11813]. This inequality is established via methods developped by the first author [arXiv:2204.02468, arXiv:2108.00555] in order to understand the symplectic geometry of certain collections of Lagrangians under metric constraints.

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