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arXiv · 2311.00467

Hofer-Zehnder capacity of magnetic disc tangent bundles over constant curvature surfaces

Johanna Bimmermann
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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.

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Johanna Bimmermann. 2023-11-01. Hofer-Zehnder capacity of magnetic disc tangent bundles over constant curvature surfaces. https://arxiv.org/abs/2311.00467

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