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.
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}
}
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9 pages