Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property

Abstract

Let $\Vert \cdot \Vert$ be a norm on ${\mathbb{R}}^N$ and let $M$ be a closed $C^1$-submanifold of ${\mathbb{R}}^N$. Consider the pointed metric space $(M,d)$, where $d$ is the metric given by $d(x,y)=\Vert x-y\Vert$, $x,y\in M$. Then the Lipschitz-free space $\mathcal{F}(M)$ has the Metric Approximation Property.

arXiv comment19 pages