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Uniqueness in mean curvature flow

In previous work, we have shown uniquess of solutions of the initial value problem for mean curvature flow in Minkowski space occurs, if we only consider uniformly spacelike or bounded solutions. We conjecture that there could be another solution if we drop uniform spacelikeness. Thus, if non-uniqueness occurs, it is only possible due to the non-compactness of the evolving hypersurfaces and the behaviour of solutions at infinity.

Our model problem is a spacelike curve (represented as the graph of a real-valued function) which we extend to more general cases once it is resolved.