Given a closed countably 1-rectifiable set in with locally finite -dimensional Hausdorff measure, we prove that there exists a Brakke flow starting from the given set with the following regularity property. For almost all time, the flow locally consists of a finite number of embedded curves of class~ whose endpoints meet at junctions with angles of either 0, 60 or 120 degrees.
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Lami Kim, Yoshihiro Tonegawa, Existence and regularity theorems of one-dimensional Brakke flows. Interfaces Free Bound. 22 (2020), no. 4, pp. 505–550DOI 10.4171/IFB/448