New obstructions to symplectic embeddings

TL;DR

This paper introduces new, stronger restrictions on symplectic embeddings of convex domains, refining existing techniques and demonstrating the sharpness of these restrictions beyond previous capacity-based limitations.

Contribution

It presents novel restrictions on symplectic embeddings that surpass Ekeland-Hofer capacities and refines Guth's embedding technique to show these are optimal.

Findings

New restrictions on symplectic embeddings of convex domains.

Restrictions are stronger than Ekeland-Hofer capacities.

Restrictions are shown to be sharp using refined techniques.

Abstract

In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.