Key points are not available for this paper at this time.
We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss curvature and make the boundary circle convex (or geodesic). The same conclusion is not known in any dimension n 3, and (by analogy with the closed case) is actually expected to be false for many values of n 4.
Carlotto et al. (Fri,) studied this question.