Fully nonlinear geometric evolution equations and global differential geometry

This project aims to apply fully nonlinear parabolic equations to obtain new results in the global differential geometry of hypersurfaces and Riemannian metrics. This work will exploit the observation that fully nonlinear equations can allow more precisely controlled behaviour than is possible in other, apparently similar equations, at the expense of only slightly greater analytical difficulty. The research is expected to yield best-possible results describing the global implications of local curvature conditions in a variety of situations, as well as advancing understanding of the regularity and asymptotic behaviour of important classes of fully nonlinear equations.