J-holomorphic cylinders between ellipsoids in dimension four

TL;DR

This paper investigates the conditions under which regular J-holomorphic cylinders can exist or not exist between nested ellipsoids in four-dimensional space, advancing understanding in symplectic geometry.

Contribution

It provides new results on the existence and nonexistence of J-holomorphic cylinders between ellipsoids in 4D, clarifying symplectic embedding constraints.

Findings

Identifies conditions for existence of J-holomorphic cylinders

Establishes nonexistence results under certain geometric configurations

Contributes to symplectic embedding theory in four dimensions

Abstract

We establish results concerning the existence and nonexistence of regular $J$-holomorphic cylinders between nested pairs of ellipsoids in $\mathbb{R}^4$.