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Hofer-Zehnder capacity of magnetic disc tangent bundles over constant curvature surfaces | | Johanna Bimmermann
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1 Nov 2023 | | Abstract: | We compute the Hofer-Zehnder capacity of magnetic disc tangent bundles over
constant curvature surfaces. We use the fact that the magnetic geodesic flow is
totally periodic and can be reparametrized to obtain a Hamiltonian circle
action. The oscillation of the Hamiltonian generating the circle action
immediately yields a lower bound of the Hofer-Zehnder capacity. The upper bound
is obtained from Lu’s bounds of the Hofer-Zehnder capacity using the theory of
pseudo-holomorphic curves. In our case the gradient spheres of the Hamiltonian
will give rise to the non-vanishing Gromov-Witten invariant needed. | | Source: | arXiv, 2311.00467 | | Services: | Forum | Review | PDF | Favorites | |
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