Asymptotic cones of injective spaces

Determine whether every asymptotic cone of an injective metric space is injective.

Background

The notes prove injectivity for asymptotic cones that are proper under a 4-hyperconvexity hypothesis, giving only a partial result toward the general asymptotic-cone question.

References

Is any asymptotic cone of an injective metric space injective? Note that we have a partial answer in Corollary~\ref{cor:asymptotic_cone_injective}.

— Group actions on injective spaces and Helly graphs  (2307.00414 - Haettel, 2023) in Section 14, “Open questions,” item 11