Department of Mathematics - Seminar on Pure Mathematics - Positivity of curvature on manifolds with boundary 

Consider two Riemannian metrics g and h on a compact manifold with smooth boundary. In this talk, we will discuss how to construct metrics which agree with h outside a neighbourhood of the boundary and agree with h in the same neighbourhood, such that the metrics constructed preserve various natural curvature conditions under suitable assumptions on the boundary data. Moreover, we will discuss how this result can be applied to preserve curvature conditions in Ricci flow on manifolds with boundary.