Abstract: Given a closed 1-rectifiable set $\Gamma_0\subset\mathbb{R}^2$ of finite 1d Hausdorff measure and a vector field $u$ in a dimensionally critical Sobolev space, we construct a non-trivial flow of curves
with the velocity given by $\kappa+u$, starting from $\Gamma_0$. The motion law is satisfied in the sense of Brakke and the flow exists through singularities. This is a joint work with Y. Tonegawa.
