Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property

Abstract: Let $|\cdot|$ 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 $d(x,y)=|x-y|$, $x,y\in M$. Then the Lipschitz-free space $\mathcal{F}(M)$ has the Metric Approximation Property.