The asymptotics of ECH capacities

  title={The asymptotics of ECH capacities},
  author={Daniel Cristofaro-Gardiner and Michael Hutchings and Vinicius G. B. Ramos},
  journal={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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