Stephen Lynch: Canonical foliation of bubblesheets

I will introduce a curvature condition for submanifolds of higher codimension which generalises constant mean curvature hypersurfaces and parallel mean curvature submanifolds. Recall that a Riemannian product is foliated by totally geodesic leaves; using the new curvature condition, these leaves can be deformed to a canonical foliation for any nearby metric. This generalises a construction used by Hamilton to canonically parameterize neck regions occurring along the Ricci flow on 3-manifolds. Our motivation is similar---to determine canonical parameterizations of more general almost-singular regions in geometric flows, such as bubblesheets.