Existence and regularity for the Brakke flow
The Brakke flow is a generalized mean curvature flow in the framework of geometric measure theory. The notion is general enough to include motion of singular objects such as networks and soap bubble clusters while it is equipped with a powerful regularity theory. I mainly explain the content of the recent existence theorem and give an outline of how to construct the time-discrete approximate flows. Ref. (1) L. Kim, Y. Tonegawa, On the mean curvature flow of grain boundaries, Ann. l’Institut Fourier (Grenoble) 67, (2017) 43-142, (2) K. Kasai, Y. Tonegawa, A general regularity theory for weak mean curvature flow, Calc. Var. PDEs 50, (2014) 1-68.