Some optimal embeddings of symplectic ellipsoids

We construct symplectic embeddings in dimension 2n ≥ 6 of ellipsoids into the product of a 4-ball or 4-dimensional cube with Euclidean space. A sequence of the embeddings are seen to be optimal by a quantitative version of the embedding obstructions introduced in [8]. In the limiting case when our ellipsoids approach a cylinder we recover an embedding of Guth, [7]. However for compact ellipsoids our embedding gives sharper results. At the other end of the scale, for certain convergent sequences of ellipsoids we reproduce estimates given by stabilizing 4-dimensional embeddings of McDuff and Schlenk, [16], in the ball case and Frenkel and Müller, [5], in the cube case.