= Hofer metric from the spatial supremum norm
{c}
{title2=$\rho_\infty(\phi,\psi)=\inf_{\phi_H^1=\phi^{-1}\psi}\int_0^1\|H_t\|_\infty\,dt$}
Use compactly supported Hamiltonians on open manifolds and zero-mean Hamiltonians on closed manifolds. Because their values straddle zero, $\|H_t\|_\infty\leq\max H_t-\min H_t\leq2\|H_t\|_\infty$. Thus $\rho_\infty\leq d_H\leq2\rho_\infty$. These are two equivalent, but not identically normalized, conventions for <Hofer's metric>. A statement about zero distance or zero displacement energy is independent of this choice.
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