10 problems

Hershkovits–White conjecture. Non-fattening level set flows must coincide with both their inner and outer flows.

Finiteness conjecture. The spacetime singular set has only finitely many connected components.

Finiteness conjecture. A mean-convex LSF has only finitely many singular times.

Let $M$ be a compact, smoothly embedded hypersurface in $\mathbf{R}^n$. Evans–Spruck's no-fattening conjecture. The level set mean curvature flow starting from $M$ never fattens, m…

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…

No-mass-drop conjecture. The Brakke flow associated to a nonfattening level set flow has no mass drop and achieves equality in the Brakke inequality.

Let $F_t(M)$ denote the level set flow starting from a closed embedded surface $M$. Its singularities are called cylindrical or spherical when their tangent flows have the correspo…

Fattening–discrepancy time conjecture. For every smooth initial surface,

Singularity obstruction conjecture. An evolving surface cannot fatten unless it has a singularity with no spacetime neighborhood in which the surface is mean convex.

Converse conjecture. If there is a unique matching Brakke flow starting from $M$, then the level set flow $F_t(M)$ is non-fattening. Equivalently, the inner and outer flows should…