Symplectic capacities of S¹-invariant dynamically convex domains in ℝ⁴

2026/06/01 by Arthur Melo, Vinicius G. B. Ramos, Alejandro Vicente · 1 voice
Mathematics · #math.SG

paper · pdf

Abstract

In this paper, we prove that all normalized symplectic capacities agree for dynamically convex domains in ℂ² that are invariant under any Hamiltonian S¹-action isotopic to the Hopf diagonal action. We also give necessary and sufficient conditions for S¹-invariant domains to be dynamically convex.

Citations

• The strong Viterbo conjecture and various flavours of duality in Lagrangian products
• A Counterexample to Viterbo's Conjecture
• Sharp systolic inequalities for invariant tight contact forms on principal S1-bundles over S2
• Zeta functions of dynamically tame Liouville domains
• On the agreement of symplectic capacities in high dimension
• Liouville-Arnold theorem for homogeneous symplectic and contact Hamiltonian systems
• Automatic transversality in contact homology II: filtrations and computations
• From Symplectic Measurements to the Mahler Conjecture
• The Conley-Zehnder index for a path of symplectic matrices
• Quantitative embedded contact homology
• The Maslov index for paths
• Normal forms for Hamiltonian systems with Poisson commuting integrals—elliptic case

Discussions

• Arthur Melo, Vinicius G. B. Ramos, Alejandro Vicente: Symplectic capacities of $S^1$-invariant dynamically convex domains in $\mathbb{R}^4$ https://arxiv.org/abs/2606.02452 https://arxiv.org/pdf/2606. [bsky, 0 points, 0 comments]

Related

• A note on symmetrical symplectic capacities
• Hopf orbits and the first ECH capacity
• Examples around the strong Viterbo conjecture
• Asymptotic Equivalence of Symplectic Capacities
• Symplectic Convexity for Orbifolds