Density and non-density of $C_c^{\infty }\hookrightarrow W^{k,p}$ on complete manifolds with curvature bounds

Shouhei Honda, Luciano Mari, Michele Rimoldi +1

We investigate the density of compactly supported smooth functions in the Sobolev space $W^{k,p}$ on complete Riemannian manifolds. In the first part of the paper, we extend to the…