Mean curvature flow of noncompact hypersurfaces with
Type-II curvature blow-up.
Abstract: The mean curvature flow (MCF) deforms a hypersurface
in the direction of its mean curvature vectors. Singularities in mean
curvature flow can form in either finite or infinite time. In this
talk, we present some results, jointly with Isenberg (Oregon) and
Zhang (Sydney), concerning the precise asymptotics of non-compact MCF
solutions with either Type-IIa (in finite time) or Type-IIb (in
infinite time) curvature blow-up. Time permitting, we also present a
numerical analysis, in collaboration with Garfinkle (Oakland
University), Isenberg (Oregon) and Knopf (UT Austin), on the stability
of Type-IIa singularity in MCF of non-compact hypersurfaces.