Title
Mean curvature flow and the direction energy
Abstract
Mean curvature flow is classically understood as the L^2-gradient flow of the volume functional. In the non-compact setting, however, this variational interpretation degenerates, since the volume is infinite and the associated energy identity becomes vacuous. In this talk, we present a new variational framework for non-compact mean curvature flow by interpreting it as the gradient flow of a direction energy. Although this functional differs from the volume by a formal null-Lagrangian, it can be finite for noncompact hypersurfaces, and enables us to study the behavior of global solutions. This is joint work with T. Miura (Kyoto).
