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arXiv · 2403.07863

Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum

Barney Bramham·Abror Pirnapasov
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Abstract

For a symplectic isotopy on the two-dimensional disc we show that the classical spectral invariants of Viterbo [20] can be extended in a meaningful way to {\it non-compactly} supported Hamiltonians. We establish some basic properties of these extended invariants and as an application we show that Hutchings' inequality in [8] between the Calabi invariant and the mean action spectrum holds without any assumptions on the isotopy; in [8] it is assumed that the Calabi invariant is less than the rotation number (or action) on the boundary.

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Barney Bramham, Abror Pirnapasov. 2024-03-12. Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum. https://arxiv.org/abs/2403.07863

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