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A classical result in Riemannian geometry states that the absolutelycontinuous curves into a (finite-dimensional) Riemannian manifold form aninfinite-dimensional manifold. In the present paper this construction andrelated results are generalised to absolutely continuous curves with values ina strong Riemannian manifolds. As an application we consider extensions of thesquare root velocity transform (SRVT) framework for shape analysis.Computations in this framework frequently lead to curves which leave the shapespace (of smooth curves), and are only contained in a completion. In the vectorvalued case, this extends the SRVT to a space of absolutely continuous curves.We investigate the situation for shape spaces of manifold valued (absolutelycontinuous) curves.

Manifolds of absolutely continuous curves and the square root velocity framework