Symplectic embeddings of polydisks

TL;DR

This paper establishes near-optimal conditions for symplectic embeddings between polydisks, relating their radii through explicit inequalities involving a constant factor, advancing understanding in symplectic geometry.

Contribution

The authors derive explicit, nearly optimal criteria for symplectic embeddings of polydisks based on their radii, improving previous bounds in symplectic embedding theory.

Findings

Embedding conditions depend on inequalities involving radii and a constant factor.

Conditions are shown to be optimal up to a constant factor.

Provides new bounds for symplectic embeddings of polydisks.

Abstract

If P is a polydisk with radii R_1 < ... < R_n and P' is a polydisk with radii R'_1 < ... < R'_n, then we construct a symplectic embedding from P into P' provided that C(n) R_1 < R'_1 and C(n) R_1 ... R_n < C(n) R'_1 ... R'_n. Up to a constant factor, these conditions are optimal.