Mathematical Research Letters

Volume 22 (2015)

Number 6

Observations on the Hofer distance between closed subsets

Pages: 1805 – 1820



Michael Usher (Department of Mathematics, University of Georgia, Athens, Ga., U.S.A.)


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 [3] and [9]. We also build on [15] to obtain new vanishing results for the Hofer distance between subsets, applicable for instance to singular analytic subvarieties of Kähler manifolds.

Accepted 7 July 2015

Published 23 May 2016