No Mass Drop for Mean Curvature Flow of Mean Convex Hypersurfaces

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Mean Curvature Flow of Higher Codimension in Hyperbolic Spaces

where H(x, t) is the mean curvature vector of Ft(M) and Ft(x) = F (x, t). We call F : M × [0, T ) → F(c) the mean curvature flow with initial value F . The mean curvature flow was proposed by Mullins [17] to describe the formation of grain boundaries in annealing metals. In [3], Brakke introduced the motion of a submanifold by its mean curvature in arbitrary codimension and constructed a genera...

Deforming Convex Hypersurfaces to a Hypersurface with Prescribed Harmonic Mean Curvature

Let F be a smooth convex and positive function defined in A = {x ∈ R : R1 < |x| < R2} satisfying F (x) ≥ nR2 on the sphere |x| = R2 and F (x) ≤ nR1 on the sphere |x| = R1. In this paper, a heat flow method is used to deform convex hypersurfaces in A to a hypersurface whose harmonic mean curvature is the given function F .

Interior Estimates and Longtime Solutions for Mean Curvature Flow of Noncompact Spacelike Hypersurfaces in Minkowski Space

Spacelike hypersurfaces with prescribed mean curvature have played a major role in the study of Lorentzian manifolds Maximal mean curvature zero hypersurfaces were used in the rst proof of the positive mass theorem Constant mean curvature hypersurfaces provide convenient time gauges for the Einstein equations For a survey of results we refer to In and it was shown that entire solutions of the m...

The Volume Preserving Mean Curvature Flow near Spheres

By means of a center manifold analysis we investigate the averaged mean curvature flow near spheres. In particular, we show that there exist global solutions to this flow starting from non-convex initial hypersurfaces.