A relative Hofer estimate and the asymptotic Hofer-Lipschitz constant

Let (M, omega) be a symplectic manifold and U subset of M an open subset. We study the natural inclusion of the compactly supported Hamiltonian group of U in the compactly supported Hamiltonian group of M. The main result is an upper bound for this map in terms of the Hofer norms for U and M. Applications are upper bounds on the asymptotic Hofer-Lipschitz constant and the relative Hofer diameter of U. The first bound is often sharp and the second one is often sharp up to a factor of 2.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

The article investigates the natural inclusion of the Hamiltonian group on a symplectic manifold, deriving an upper bound based on Hofer norms. This leads to upper bounds on the asymptotic Hofer-Lipschitz constant and the relative Hofer diameter of a subset, typically with the first bound being sharp and the second one being sharp up to a factor of 2.