Inverse anisotropic mean curvature flow and a Minkowski type inequality

Anisotropic and Crystalline Mean Curvature Flow

The Brunn-Minkowski-Type Inequality

Mean Curvature Blowup in Mean Curvature Flow

In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.

the brunn-minkowski-type inequality

The Inverse Mean Curvature Flow in Cosmological Spacetimes

We prove that the leaves of an inverse mean curvature flow provide a foliation of a future end of a cosmological spacetime N under the necessary and sufficent assumptions that N satisfies a future mean curvature barrier condition and a strong volume decay condition. Moreover, the flow parameter t can be used to define a new physically important time function.