Observations on the Hofer distance between closed subsets

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.

9 pages

References in corpus (1)

• C^0-rigidity of Poisson brackets

Cited by in corpus (6)

• Bounds on spectral norms and barcodes
• Local rigidity, contact homeomorphisms, and conformal factors
• Local rigidity, symplectic homeomorphisms, and coisotropic submanifolds
• The $\gamma$-support as a micro-support
• Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
• $C^0$-limits of Legendrians and positive loops