LAUSR

Abstract The convex cone S C SLip 1 ( X ) of real-valued smooth semi-Lipschitz functions on a Finsler manifold X is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of X . In this work we show that the subset of smooth semi-Lipschitz functions of constant strictly less than 1, denoted S C 1 − 1 ( X ) , can be used to classify Finsler manifolds and to characterize almost isometries between them, in the lines of the classical Banach-Stone and Mykers-Nakai theorems.