Singularity formation in fully nonlinear flows of hypersurfaces
The partial differential equations and analysis seminar is the research seminar associated with the applied and nonlinear analysis, and the analysis and geometry programs.
Abstract: We consider curvature flows of hypersurfaces in a Riemannian manifold. An important example is the flow by mean curvature, but for many geometric problems flows by other speeds have proven to be a more effective tool. The key step for most applications is to understand the structure of singularities. We will discuss a new a priori 'convexity' estimate, which implies that singularities are positively curved, even if the initial datum is highly non-convex. As a consequence, we obtain a complete classification of Type I singularities under very general conditions, despite having no analogue of Huisken's monotonicity formula for mean curvature flow.
The Zoom link for this talk is available here. If you are not currently affiliated with the ANU, please contact Po-Lam Yung for access.
Zoom / Seminar Room 1.33