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arXiv · 0808.1592

The sharp energy-capacity inequality

Michael Usher
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Abstract

Using the Oh-Schwarz spectral invariants and some arguments of Frauenfelder, Ginzburg, and Schlenk, we show that the \pi_1-sensitive Hofer-Zehnder capacity of any subset of a closed symplectic manifold is less than or equal to its displacement energy. This estimate is sharp, and implies some new extensions of the Non-Squeezing Theorem.

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Michael Usher. 2008-08-11. The sharp energy-capacity inequality. https://arxiv.org/abs/0808.1592

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