Let $D^2 \subset \mathbb{R}^2$ the unit disk and $f: D^2 \rightarrow D^2$ a homeomorphism with the property that $f$ restricted to the boundary $\partial D^2$ is the identity. Then $f$ is ambient isotopic to the identity.
I know the Annulus Theorem and I can use it to ambient isotope $f$ to the identity on any circle inside $D^2$, but I have no clue how to extend it such that it turns f to the identity on an open set around this circle or even construct the isotopy that works for the whole $D^2$.