The constant angle problem for mean curvature flow inside rotational tori

We flow a hypersurface in Euclidean space by mean curvature flow (MCF) 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 MCF exists for all time and converges to a flat cross-section as $t \to \infty$.

2010 Mathematics Subject Classification

35K59, 53C17, 53C44

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Accepted 18 November 2013

Published 13 October 2014