Gromov's Non-Squeezing Theorem and Beltrami type equation

TL;DR

The paper presents a new method for constructing J-complex discs using Beltrami equations, providing a concise proof of Gromov's Non-Squeezing Theorem through this approach.

Contribution

It introduces a novel technique for constructing J-complex discs based on Beltrami equations, simplifying the proof of a fundamental symplectic geometry result.

Findings

Constructed J-complex discs using Beltrami equations

Provided a short, self-contained proof of Gromov's Non-Squeezing Theorem

Demonstrated the effectiveness of the method in symplectic topology

Abstract

We introduce a method for constructing J-complex discs. The method only uses the standard scheme for solving the Beltrami equation and the Schauder principle. As an application, we give a short self-contained proof of Gromov's Non-Squeezing Theorem.