12 problems

A pitchfork is the complete translating soliton obtained by reflecting a fundamental graph over the strip $(0,w)\times\mathbb{R}$, where $w\geq\pi$, with the pitchfork boundary val…

Let $v$ be a unit vector and let $\Sigma={\rm Graph}_{(v,\Omega)}[u]$ be a complete connected translating graph over a connected planar domain $\Omega\subseteq[v]^\perp$. The domai…

For $w\geq\pi$, let $u:(0,w)\times\mathbb{R}\to\mathbb{R}$ solve the pitchfork boundary-value problem … The reflected graph is a complete simply connected translating soliton of fi…

A translating graph is a surface of the form $\Sigma=\{p+u(p)v:p\in\Omega\}$, where $\Omega$ is an open planar domain in $[v]^\perp$, and its domain is contained in a planar strip…

Let $n\geq 2$ and let $\alpha<\frac{1}{n+2}$. An $\alpha$-translator is a translating soliton in $\mathbb{R}^{n+1}$ for the power of Gauss curvature specified in the paper, and an…

Let $M$ be a complete translating soliton in $\mathbb{R}^{n+k}$. At points where the mean-curvature direction $\xi=-\vec{H}/|H|$ is defined, the property that … equivalently, that…

Stable translating soliton classification conjecture. Then $\Sigma$ is mean convex and, up to an ambient isometry, is one of the following translating solitons:

Low-entropy mean-convexity conjecture. Then $\Sigma$ is mean convex.

The paper considers a translating hypersurface $M$ asymptotic to half-hyperplanes in a vertical cylinder, meaning that the cylinder axis is parallel to the translating velocity. Th…

Wang's conjecture. For $n=2$, any entire graphical translating soliton must be locally strictly convex. In dimensions $n>2$, the analogous statement should hold under the additiona…

Let $u$ be a solution of … where $C>1$ and the graph of $u$ is an entire strictly spacelike hypersurface in Minkowski space. Aarons's conjecture. The solution $u$ is either rotatio…

A hypersurface $M^n\subset\mathbb{R}^{n+1}$ is a translating soliton if its mean curvature $H$ and unit normal vector $\nu$ satisfy … for some nonzero $V\in\mathbb{R}^{n+1}$. Such…