Asymptotically Mean Value Harmonic Functions in Subriemannian and RCD Settings

Abstract We consider weakly and strongly asymptotically mean value harmonic (amv-harmonic) functions on subriemannian RCD settings. demonstrate that, in non-collapsed RCD-spaces with vanishing metric measure boundary, Cheeger are amv-harmonic Carnot groups, weak amv-harmonicity equivalently characterizes harmonicity the sense of sub-Laplacian. In homogeneous groups step 2, we prove a Blaschke–Privaloff–Zaremba type theorem. Similar results discussed settings Riemannian manifolds for Alexandrov surfaces.