Minkowski metric measure structures are infinitesimally Hilbertian

A canonical infinitesimally Hilbertian structure on locally Minkowski spaces

The aim of this paper is to show the existence of a canonical distance
$\mathsf d'$ defined on a locally Minkowski metric measure space $(\mathsf
X,\mathsf d,\mathfrak m)$ such that:
i) $\mathsf d'$ is equivalent to $\mathsf d$,
ii) $(\mathsf X, \mathsf d', \mathfrak m)$ is infinitesimally Hilbertian.
This new regularity assumption on $(\mathsf X, \mathsf d,\mathfrak m)$
essentially forces the structure to be locally similar to a Minkowski space and
defines a class of metric measure structures which includes all the Finsler
manifolds, and it is actually strictly larger. The required distance $\mathsf
d'$ will be the intrinsic distance $\mathsf d_\mathsf{KS}$ associated to the
so-called Korevaar-Schoen energy, which is proven to be a quadratic form. In
particular, we show that the Cheeger energy associated to the metric measure
space $(\mathsf X, \mathsf d_\mathsf{KS}, \mathfrak m)$ is in fact the
Korevaar-Schoen energy.