Low regularity function spaces of $N$-valued maps are contractible - Mironescu, Petru (MATHEMATICA SCANDINAVICA, 2017)
Let $M$ be a compact Lipschitz submanifold, possibly with boundary, of $\mathbb{R} ^n$. Let $N\subset \mathbb{R} ^k$ be an arbitrary set. Let $s\ge 0$ and $1\le p<∞ $ be such that $sp<1$. Then $W^{s, p}(M ; N)$ is contractible.