  We give a new proof for the existence of mean curvature flow with surgery of
2-convex hypersurfaces in $R^N$, as announced in arXiv:1304.0926. Our proof
works for all $N \geq 3$, including mean convex surfaces in $R^3$. We also
derive a priori estimates for a more general class of flows in a local and
flexible setting.

Differential Geometry;Analysis of PDEs