# The asymptotics of ECH capacities

@article{CristofaroGardiner2012TheAO,
title={The asymptotics of ECH capacities},
author={Daniel Cristofaro-Gardiner and Michael Hutchings and Vinicius G. B. Ramos},
journal={Inventiones mathematicae},
year={2012},
volume={199},
pages={187-214}
}
• Published 8 October 2012
• Mathematics
• Inventiones mathematicae
In a previous paper, the second author used embedded contact homology (ECH) of contact three-manifolds to define “ECH capacities” of four-dimensional symplectic manifolds. In the present paper we prove that for a four-dimensional Liouville domain with all ECH capacities finite, the asymptotics of the ECH capacities recover the symplectic volume. This follows from a more general theorem relating the volume of a contact three-manifold to the asymptotics of the amount of symplectic action needed…
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