Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian

In this paper, we study some potential-theoretic aspects of the eikonal and infinity Laplace operator on a Finsler manifold M. Our main result shows that forward completeness M can be detected in terms Liouville properties maximum principles at for subsolutions suitable inequalities, including Δ∞Nu≥g(u). Also, an ∞-capacity criterion viscosity version Ekeland principle are proved to equivalent Part proof hinges new boundary-to-interior Lipschitz estimate solutions Δ∞Nu=g(u) relatively compact sets, implies uniform certain entire, bounded without requiring