Quantitative $h$-principle for isotropic embeddings and applications to $C^0$-symplectic geometry

Understand

We prove here a quantitative $h$-principle statement that applies to isotropic embeddings of discs.

• We then apply it to get $C^0$-flexibility and rigidity results in symplectic geometry.
• On the flexible side, we prove that a symplectic homeomorphism might take a symplectic disc to a smooth isotropic one.
• We also get a $C^0$-rigidity result for the action of a symplectic homeomorphism on the reduction of a coisotropic submanifold.