This research demonstrates the link between spacetime brakke flow and mean curvature flow, suggesting new insights into geometric measure theory.
We prove that the spacetime Brakke flow constructed by Buet et al. is non-trivial as long as the initial varifold is a union of boundaries of domains of finite perimeter. In the codimension 1 setting, we show that, starting from a smooth boundary, the support of the mass measure of the spacetime Brakke flow coincides with the support of the classical mean curvature flow.
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Abdelmouksit Sagueni (2025) studied this question.
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