Sharp symplectic embeddings of cylinders

TL;DR

This paper demonstrates that certain high-dimensional symplectic cylinders can be embedded into products of balls and Euclidean spaces with a specific radius threshold, advancing understanding of symplectic embedding constraints.

Contribution

It establishes a new embedding result for cylinders into products of balls and Euclidean spaces with a minimal radius R of at least , improving previous bounds.

Findings

Embedding of Z^{2n}(1) into B^4(R) imes R^{2(n-2)} for R \u2265 

Minimal radius R for embedding is 

Extension of symplectic embedding techniques to higher dimensions

Abstract

We show that the cylinder Z^{2n}(1):= B^2(1)\times \mathbb{R}^{2(n-1)} embeds symplectically into B^4(R) \times \mathbb{R}^{2(n-2)} if R \geq \sqrt{3}.