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Curves and Networks in Geometric Analysis

On the mean curvature flow of grain boundaries

speaker: Lami Kim (Tokyo Institute of Technology)

abstract: Suppose that $\Gamma_{0\subset\mathbb} R^{n+1}$ is a closed countably $n$-rectifiable set whose complement $\mathbb R^{{n+1}\setminus} \Gamma_0$ consists of more than one connected component. Assume that the $n$-dimensional Hausdorff measure of $\Gamma_0$ is finite or grows at most exponentially near infinity. Under these assumptions, we prove a global-in-time existence of mean curvature flow in the sense of Brakke starting from $\Gamma_0$. There exists a finite family of open sets which move continuously with respect to the Lebesgue measure, and whose boundaries coincide with the space-time support of the mean curvature flow. This is a joint work with Prof. Yoshihiro Tonegawa.

timetable:
Wed 28 Jun, 10:30 - 11:20, Aula Dini
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