Wiener criterion on metric spaces: Boundary regularity in axiomatic and poincaré-sobolev spaces

We obtain a Wiener-type criterion for the Hölder continuity of extremal functions on general metric spaces in an abstract setting. Then we use this result to establish the boundary regularity of quasi-minimizers of the p-energy integral in the axiomatic framework of Gol'dshtein-Troyanov and also for extremal functions from the class of Poincaré-Sobolev functions.