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I want to show that the energy displacement of [itex]Z^{2n}(r)[/itex], the 2n-dimensional cylinder with radial radius is at most [itex]\pi r^2[/itex].
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, [itex]d_H(Id,ϕ)[/itex] where ϕ is a translation s.t ϕ(B2(r)×K)∩(B2(r)×K)=∅, where [itex]K \subset \mathbb{R}^{2n-2}[/itex].
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?
Thanks in advance.
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, [itex]d_H(Id,ϕ)[/itex] where ϕ is a translation s.t ϕ(B2(r)×K)∩(B2(r)×K)=∅, where [itex]K \subset \mathbb{R}^{2n-2}[/itex].
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?
Thanks in advance.