Quantitative $h$-principle in symplectic geometry

TL;DR

This paper establishes a quantitative $h$-principle for subcritical isotropic embeddings in symplectic geometry and demonstrates its application by constructing a symplectic homeomorphism in higher dimensions.

Contribution

It introduces a quantitative $h$-principle for isotropic embeddings and applies it to construct specific symplectic homeomorphisms in dimensions six and above.

Findings

Proved a quantitative $h$-principle for subcritical isotropic embeddings.

Constructed a symplectic homeomorphism mapping a symplectic disc to an isotropic one.

Extended results to symplectic manifolds of dimension at least 6.

Abstract

We prove a quantitative $h$-principle statement for subcritical isotropic embeddings. As an application, we construct a symplectic homeomorphism that takes a symplectic disc into an isotropic one in dimension at least $6$.