Existence of multi-phase Brakke flow starting from closed rectifiable set
Suppose that we are given an arbitrary closed countably n-rectifiable set in the n+1 dimensional Euclidean space. Suppose the set has the n-dimensional Hausdorff measure growing at most exponentially near infinity and suppose that the complement has more than one connected component. In my joint work with Lami Kim, we prove a time-global existence result of Brakke flow starting from such set by modifying Brakke's original time-discrete construction scheme. I will present the exact statement of the result and the relevant partial regularity theorems, and then give an outline of the existence proof.