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arXiv · 1911.07991

Smooth semi-Lipschitz functions and almost isometries of Finsler manifolds

Aris Daniilidis·Jesus Jaramillo·Francisco Venegas M
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Abstract

The convex cone $SC_{\mathrm{SLip}}^1(\mathcal{X})$ of real-valued smooth semi-Lipschitz functions on a Finsler manifold $\mathcal{X}$ is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of $\mathcal{X}$. In this work we show that the subset of smooth semi-Lipschitz functions of constant strictly less than $1$, denoted $SC_{1^{-}}^1(\mathcal{X})$, 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.

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Aris Daniilidis, Jesus Jaramillo, Francisco Venegas M. 2019-11-18. Smooth semi-Lipschitz functions and almost isometries of Finsler manifolds. https://arxiv.org/abs/1911.07991

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