Weak density of smooth maps in \(W^{1, 1}(M,N)\) for non-Abelian \({\pi}_1(N)\)
Let \(M\) and \(N\) be smooth compact Riemannian manifolds such that \(N\) is closed and isometricly embedded in \({\mathbb R}^N\). Set \[ W^{1,1}(M,N):=\{u\in W^{1,1}(M,{\mathbb R}^N); u(x)\in N \text{ for a.e. } x\in M\}. \] In this paper the author proves that smooth maps are dense in the sense of biting convergence in \(W^{1,1}(M,N)\) (Theorem 1).
scientific article; zbMATH DE number 1901460