For any convex toric domain, the liminf of the subleading ECH capacities equals minus half the affine perimeter, yielding new packing obstructions and a classification of smooth toric domains with infinite staircases.
Blair, The ‘Total Scalar Curvature’ as a symplectic invariant, and related results, Proceedings of the 3rd Congress of Geometry (Thessaloniki, 1991), Aristotle Univ
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Curvy points, the perimeter, and the complexity of convex toric domains
For any convex toric domain, the liminf of the subleading ECH capacities equals minus half the affine perimeter, yielding new packing obstructions and a classification of smooth toric domains with infinite staircases.