Mathematical Research Letters
Volume 22 (2015)
Observations on the Hofer distance between closed subsets
Pages: 1805 – 1820
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  and . We also build on  to obtain new vanishing results for the Hofer distance between subsets, applicable for instance to singular analytic subvarieties of Kähler manifolds.