Anisotropic mean curvature flow in higher codimension

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...

Mean Curvature Flows in Higher Codimension

The mean curvature flow is an evolution process under which a sub-manifold deforms in the direction of its mean curvature vector. The hypersurface case has been much studied since the eighties. Recently, several theorems on regularity, global existence and convergence of the flow in various ambient spaces and codimensions were proved. We shall explain the results obtained as well as the techniq...

Level set approach to mean curvature flow in arbitrary codimension

We develop a level set theory for the mean curvature evolution of surfaces with arbitrary co-dimension, thus generalizing the previous work [6, 13] on hypersurfaces. The main idea is to surround the evolving surface of co-dimension k in R by a family of hypersurfaces (the level sets of a function) evolving with normal velocity equal to the sum of the (d − k) smallest principal curvatures. The e...

Anisotropic and Crystalline Mean Curvature Flow

Flow by mean curvature of surfaces of any codimension