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 ...

An oriented k-coloring of an oriented graph ~ G = (V, ~ E) is a partition of V into k subsets such that there are no two adjacent vertices belonging to the same subset and all the arcs between a pair of subsets have the same orientation. The decision problem k-oriented chromatic number (ocnk) consists of an oriented graph ~ G and an integer k > 0, plus the question if there exists an oriented k...