Special Solutions and Global Behaviour

Abstract

Definition 2.1 (Mean Curvature Flow) A family of smoothly embedded hypersurfaces (Mt)t∈I in R^{n +1} moves by mean curvature if

$$ \frac{{\partial x}} {{\partial t}} = \vec H(x) $$

((2.1))

for x ∈ Mt and t ∈ I, I ⊂ R an open interval. Here $\vec H(x)$ is the mean curvature vector at x ∈ Mt.