8 problems

A translator is a translating solution of Gauss curvature flow, represented as a graph over a domain $\Omega\subset \mathbb{R}^2$. The boundary $\partial\Omega$ is the boundary of…

Let $w$ be a width, and let $\Sigma_w$ denote the corresponding semigraphical translator: a helicoid when $w<\pi$ and a pitchfork when $w\geqslant\pi$. Uniqueness conjecture. For a…

Let $\mathcal A$ be the family of annuloids in $\mathbf{R}^3$, and let $x(M)$ denote the necksize and $b(M)$ the inner width of an annuloid $M$. Fix $R>0$ and suppose that…

Let $s>0$ be fixed, and let $M_i$ be an annuloid in the family $mathcal A$ from Corollary, with necksize $s$ and inner width $b_i\to\infty$. After suitable vertical translations, c…

Let $T[\Sigma_0]$ denote the level-set flow associated with the translator $\Sigma_0$, and suppose that $T[\Sigma_0]$ fattens. A complete translator is called unstable or mathcal{I…

Let the complete translators constructed in Theorem be the finite-entropy translating hypersurfaces obtained there. Type-II blow-up conjecture. The complete translators constructed…

Let $M$ be a semigraphical translator over the strip $\Omega=\mathbf{R}\times(0,b)$, where $b\geq\pi$, such that the set of boundary points whose vertical lines lie in $M$ consists…

A blowup is a tangent-flow limit obtained by rescaling an embedded mean curvature flow near a singularity; such a blowup is non-collapsed if it satisfies the relevant uniform inter…