The sharp energy-capacity inequality

Details The sharp energy-capacity inequality The sharp energy-capacity inequality

2008-08-11

arxiv.org/abs/0808.1592v1

Commun. Contemp. Math. 12 (2010), no. 3, 457--473

Mathematics

Symplectic Geometry

14 pages

Scientific paper

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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