# Question on energy displacement.

1. May 19, 2012

### MathematicalPhysicist

I want to show that the energy displacement of $Z^{2n}(r)$, the 2n-dimensional cylinder with radial radius is at most $\pi r^2$.

In the textbook of Mcduff and Salamon they write that I should identify the two dimensional ball (with radius r) with a square of the same area, and then calculate Hofer's metric, $d_H(Id,ϕ)$ where ϕ is a translation s.t ϕ(B2(r)×K)∩(B2(r)×K)=∅, where $K \subset \mathbb{R}^{2n-2}$.

I don't know how to calculate Hofer's metric, I mean it depends on the Hamiltonian here, and I don't know how does it look here?