Relative Hofer Geometry and the Asymptotic Hofer-Lipschitz Constant

Details Relative Hofer Geometry and the Asymptotic Hofer-Lipschitz Constant Relative Hofer Geometry and the Asymptotic Hofer-Lipschitz Constant

2011-02-24

arxiv.org/abs/1102.4892v2

Mathematics

Symplectic Geometry

44 pages, 2 figures. I added a discussion of Corollary 4 and Theorem 5

Scientific paper

Let $(M,\omega)$ be a symplectic manifold and $U\subseteq M$ an open subset. I study the natural inclusion of the group of Hamiltonian diffeomorphisms of $U$ into the group of Hamiltonian diffeomorphisms 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 relative Hofer diameter of $U$ and the asymptotic Hofer-Lipschitz constant, which are often sharp up to constant factors. As another consequence, the relative Hofer diameter of certain symplectic submanifolds vanishes.

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