Smooth semi-Lipschitz functions and almost isometries between Finsler manifolds

Abstract

The convex cone SC1 SLip(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 SC1 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.