Coisotropic Displacement and Small Subsets of a Symplectic Manifold

Abstract

We prove a coisotropic intersection result and deduce the following: 1. Lower bounds on the displacement energy of a subset of a symplectic manifold, in particular a sharp stable energy-Gromov-width inequality. 2. A stable non-squeezing result for neighborhoods of products of unit spheres. 3. Existence of a "badly squeezable" set in ${\mathbb{R}}^{2n}$ of Hausdorff dimension at most $d$, for every $n\ge 2$ and $d\ge n$. 4. Existence of a stably exotic symplectic form on ${\mathbb{R}}^{2n}$, for every $n\ge 2$. 5. Non-triviality of a new capacity, which is based on the minimal symplectic area of a regular coisotropic submanifold of dimension $d$.

arXiv comment34 pages

References in corpus (1)

• Hofer Geometry of a Subset of a Symplectic Manifold