A H\"older-type inequality for the Hausdorff distance between Lagrangians

TL;DR

This paper establishes a H"older-type inequality relating the Hausdorff distance and spectral or Hofer-Chekanov distances between Lagrangian submanifolds, advancing the understanding of their symplectic geometry under metric constraints.

Contribution

It introduces a novel H"older-type inequality for Lagrangians, connecting geometric and spectral distances, based on advanced methods in symplectic geometry.

Findings

Proves a H"older-type inequality for Lagrangian distances.

Links Hausdorff distance with spectral and Hofer-Chekanov distances.

Enhances understanding of Lagrangian geometry under metric constraints.

Abstract

We prove a H\"older-type inequality for the Hausdorff distance between Lagrangians with respect to the Lagrangian spectral distance or the Hofer-Chekanov distance in the spirit of Joksimovi\'c-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.