Stability of manifold-valued subdivision schemes and multiscale transformations (Q607487)

It is well known that along with a linear subdivision scheme a multiscale transformation is defined, such transformation can also be defined in nonlinear setting. Here the author introduces a new kind of proximity condition which bounds the difference of the differential of a nonlinear subdivision scheme and a linear one. It turns out that-unlike the generic nonlinear case and modulo some minor technical assumptions in the manifold-valued setting, convergence implies stability of the nonlinear subdivision scheme and associated nonlinear multiscale transformations.