Hamiltonian dynamics and symplectic capacities
Résumé
We show that the cylinder B^2(1) \times \mathbb{R}^{2(n-1)} embeds symplectically into the product B^{2(n-1)}(R) \times \mathbb{R}^2 for some finite R>0, which answers a question posed by H. Hofer in 1989. This implies the nonexistence of symplectic d-capacities, 1\sqrt{3}. We supply the final arguments to answer Hofer's questions. The main tool is a construction to remove singular limits of families of embeddings.