Existence of the theory of infinity-harmonic functions for general Riemannian metrics

Let $(M,g)$ be a Riemannian manifold, and consider $\infty$-harmonic functions and the associated notions of viscosity solutions, comparison with cones, gradient estimates, and regularity. General-metric infinity-harmonic theory conjecture. The theory of $\infty$-harmonic functions for general Riemannian metrics should be developed; most known results, including the theorems on gradients and regularity results cited in the source, should carry over. In particular, Theorem~ should hold for every Riemannian manifold $(M,g)$. The paper explains that its results use only a preliminary theory for hyperbolic metrics, while the corresponding theory for variable metrics is largely undeveloped.