TITLE: What results are immediately generalised to higher dimensions, in light of Schoen and Yau's recent preprint?
QUESTION [46 upvotes]: Many problems in geometric analysis and general relativity have been established in dimensions $3\leq n\leq 7$, as the regularity theory for minimal hypersurfaces holds up to dimension 7*. In a recent preprint, Schoen and Yau show how the usual techniques can be generalised to arbitrary dimension.

My question is: What known results can trivially said to be true in higher dimensions now, in light of this paper? Also, which related results with the same dimension restriction will be non-trivial to extend to higher dimensions?

Apologies if this question is too open-ended (this is my first time posting here) – I'm hoping it will be considered something like a "community wiki", as I think such a list would be interesting to the community.
*More precisely, see Thompson's comment below

REPLY [4 votes]: The progress of Schoen and Yau also allows to generalize many statements previously known only for spin manifolds to non-spin manifolds. See e.g. a preprint by Thomas Schick and Simone Cecchini, arXiv  math.GT 1810.02116. In particular, they are now able to prove the following:
An enlargeable metric (complete or not) cannot have uniformly positive scalar curvature. Therefore, a closed enlargeable manifold cannot carry any metric of positive scalar curvature.