Symplectic capacities of $S^1$-invariant dynamically convex domains in $\mathbb{R}^4$

Alejandro Vicente; Arthur Melo; Vinicius G. B. Ramos

arxiv: 2606.02452 · v1 · pith:D5N6SPSDnew · submitted 2026-06-01 · 🧮 math.SG

Symplectic capacities of S¹-invariant dynamically convex domains in mathbb{R}⁴

Arthur Melo , Vinicius G. B. Ramos , Alejandro Vicente This is my paper

classification 🧮 math.SG

keywords convexdomainsdynamicallyinvariantactioncapacitiesmathbbsymplectic

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In this paper, we prove that all normalized symplectic capacities agree for dynamically convex domains in $\mathbb{C}^2$ that are invariant under any Hamiltonian $S^1$-action isotopic to the Hopf diagonal action. We also give necessary and sufficient conditions for $S^1$-invariant domains to be dynamically convex.

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Symplectic capacities of S¹-invariant dynamically convex domains in mathbb{R}⁴

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