Some optimal embeddings of symplectic ellipsoids

TL;DR

This paper constructs optimal symplectic embeddings of high-dimensional ellipsoids into products involving 4-dimensional shapes and Euclidean space, advancing understanding of symplectic embedding problems.

Contribution

It introduces new constructions of symplectic embeddings for ellipsoids in dimensions six and higher, demonstrating their optimality.

Findings

Embeddings of high-dimensional ellipsoids into product spaces are constructed.

A sequence of embeddings is proven to be optimal.

The work extends symplectic embedding theory to higher dimensions.

Abstract

We construct symplectic embeddings of ellipsoids of dimension $2n \ge 6$ into the product of a 4-ball or 4-dimensional cube with Euclidean space. A sequence of these embeddings can be shown to be optimal.