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.

中文翻译：

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平滑的半李普希茨函数和芬斯勒流形之间的几乎等距

摘要 Finsler 流形 X 上实值光滑半Lipschitz 函数的凸锥SC SLip 1 ( X ) 是一种阶代数结构，它同时捕获了X 的可微特征和拟度量特征。在这项工作中，我们展示了常数严格小于 1 的光滑半李普希茨函数的子集，表示为 SC 1 − 1 ( X ) ，可用于对 Finsler 流形进行分类并表征它们之间的几乎等距，在经典的 Banach-Stone 和 Mykers-Nakai 定理。