English

Observations on the Hofer distance between closed subsets

Symplectic Geometry 2016-08-10 v1

Abstract

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 subvarieties of Kahler manifolds.

Keywords

Cite

@article{arxiv.1409.2577,
  title  = {Observations on the Hofer distance between closed subsets},
  author = {Michael Usher},
  journal= {arXiv preprint arXiv:1409.2577},
  year   = {2016}
}

Comments

9 pages

R2 v1 2026-06-22T05:52:00.030Z