5 problems

For every closed smooth strong spacelike curve $\gamma_0\subset\mathbb{R}^{2,q}$ of index $1$, the solution $\gamma(\cdot,t)$ of the usual curve-shortening flow exists up to a fini…

Let $\phi$ be a smooth, strictly convex norm on $\mathbf{R}^{n+1}$, with Wulff shape $\mathcal{W}^\phi=\{x\in\mathbf{R}^{n+1}:\phi^*(x)=1\}$. Let $X_0:M\to\mathbf{R}^{n+1}$ be a cl…

Let $m\geq0$ and $N_0\geq2$, where $N_0$ is the rotation number of the initial immersed curve. Consider the area-preserving curvature flow of order $m$. Finite-time blowup conjectu…

Let $m\geq1$. Consider the area-preserving curvature flow of order $m$ for embedded initial curves with length $L_0$ and enclosed area $1$. Immortal-solution conjecture. For every…

Let $G$ be the curvature function defining the flow, and consider convex ancient $G$-flows that are noncollapsing, uniformly two-convex, and compact. Uniqueness conjecture. Up to p…