take this opportunity to state and discuss [*some new interesting research lines*]{} opened by the results obtained in the present paper.

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In the setting of Theorem \[NLMS\], can one construct examples in which $f'(\zeta)=\pm\infty$ for some $\zeta\in\left(-\frac32,\frac32\right)$?

Namely, is it possible to construct examples of nonlocal minimal graphs embedded in ${\ensuremath{\mathbb{R}}}^3$ which are flat from outside and whose trace develops vertical tangencies?

The trace of such possible pathological examples is depicted in Figure \[DOMA-122\].

![*[[Open problem \[16\]: is it possible to construct nonlocal minimal graphs traces with vertical tangencies?]{}]{}*[]{data-label="DOMA-122"}](traccia-3.pdf){width="8.9cm"}

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It would be interesting to determine whether or not a result similar to Theorem \[NLMS\] holds true in higher dimension. Similarly, it would be interesting to determine the possible validity of Theorem \[QC\] in higher dimensions.

[F]{}rom the technical point of view, we observe that some of the auxiliary results exploited towards the proof of Theorem \[QC\] (such as Lemma \[STEP1\] and Corollary \[STEP11\]) are expected to carry over in higher dimension, therefore one can in principle try to argue by induction, supposing that a statement such as the one of Theorem \[QC\] holds true in dimension $n$ with the aim of proving it in dimension $n+1$. The catch 