Theorem 1.1 limit-shape conjecture for general rate vectors

Let $\vec{\mathbf{r}}\in\mathscr{R}$ be a rate vector, let $N\geq1$, and suppose that $N^2T\to\infty$. Theorem 1.1 concerns the spacetime limit shape of the KPZ equation in the upper-tail regime.

Theorem 1.1 limit-shape conjecture. The results of Theorem 1.1 hold for all $\vec{\mathbf{r}}\in\mathscr{R}$ under $N\geq1$ and $N^2T\to\infty$.

This extends the theorem beyond the parameter regime established in the paper. The surrounding discussion states that the limiting shape should still be described by the entropy solution of the backward equation with the corresponding terminal condition, while the behavior outside the concavity region is more complicated.