Symplectic embeddings from R²ⁿ into some manifolds

Abstract

We show by elementary methods that there are symplectic embeddings from standard (R²ⁿ, ω₀) into (Σ x R²ⁿ⁻², ω ⊕ ω₀) and (T^2n−2k x R^2k, ω ⊕ ω₀), where (Σ, ω) is a closed two-dimensional symplectic manifold, and (T^2n−2k, ω) is the torus with a constant symplectic form ω. Some estimates of Gromov's symplectic capacity are given for bounded domains in these manifolds.