Local pinching estimates for fully nonlinear curvature flows

Improvement-of-pinching estimates are a crucial tool in the analysis of singularities in geometric flows. They assert that certain scale-invariant curvature inequalities tend to improve as curvature blows-up, providing a great deal of control on the geometry at a singularity. I will give a brief overview of such estimates, before showing how to localize them. I will then describe some applications.

This is joint work with James McCoy.