A Hölder-type inequality for the Hausdorff distance between Lagrangians.

Abstract

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.