Observations on the Hofer distance between closed subsets

@inproceedings{Usher2015ObservationsOT,
  title={Observations on the Hofer distance between closed subsets},
  author={Michael Usher},
  year={2015}
}
We prove the elementary but surprising fact that the Hofer distance between two closed subsets of a symplectic manifold can be expressed in terms of the restrictions of Hamiltonians to one of the subsets; this helps explain certain energy-capacity inequalities that appeared recently in work of Borman-McLean and Humiliere-Leclercq-Seyfaddini. We also build on arXiv:1201.2926 to obtain new vanishing results for the Hofer distance between subsets, applicable for instance to singular analytic… CONTINUE READING