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arXiv · 2608.19042

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

Gabriel Beiner
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Abstract

We show that the ECH capacities of every closed symplectic 4-manifold with a rational symplectic form 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.

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Gabriel Beiner. 2026-08-19. The ECH and alternative ECH capacities of closed symplectic 4-manifolds. https://arxiv.org/abs/2608.19042

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