Existence of graphical tangents in the original infinite-dimensional target

Determine whether graphical tangents of Lipschitz maps from metric measure spaces into an infinite-dimensional Banach space can exist with the same target space as the original map, rather than only in an ultrapower of that Banach space.

Background

The paper defines a graphical tangent of a mapping package as a graphical limit of rescaled maps along a sequence of radii tending to zero. For maps into a Banach space V, the natural target of an ultralimit is generally the ultrapower V^\omega. The authors explain that imposing the additional requirement that tangent maps take values in the original target V is too restrictive when V is infinite dimensional, and they explicitly state that they do not know whether any such tangents exist. The open problem is therefore to settle existence under this same-target constraint.