The ECH and alternative ECH capacities of closed symplectic 4-manifolds

Abstract

We show that the ECH capacities of every closed symplectic 4-manifold are infinite. We also give the first examples of symplectic 4-manifolds whose alternative ECH capacities are infinite. We verify the ECH Weyl law holds with bounded subleading asymptotics for the alternative ECH capacities of any closed symplectic 4-manifold with $b_2^+=1$ or any smooth domain therewithin.