The constant angle problem for mean curvature flow inside rotational tori

Abstract

We flow a hypersurface in Euclidean space by mean curvature flow with a Neumann boundary condition, where the boundary manifold is any torus of revolution. If we impose the conditions that the initial manifold is compatible and does not contain the rotational vector field in its tangent space, then mean curvature flow exists for all time and converges to a flat cross-section as $t \rightarrow \infty$.