Density and non-density of Cc∞↪Wk,p on complete manifolds with curvature bounds

• Published in: Nonlinear analysis Vol. 211
• Main Authors: Honda, Shouhei, Mari, Luciano, Rimoldi, Michele, Veronelli, Giona
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2021
• Subjects: Alexandrov space; Curvature; Density; RCD space; Sampson formula; Singular point; Sobolev space; 46E35; Sobolev space; 53C21; Singular point; Sampson formula; Density; Curvature; Alexandrov space; RCD space

We investigate the density of compactly supported smooth functions in the Sobolev space Wk,p on complete Riemannian manifolds. In the first part of the paper, we extend to the full range p∈[1,2] the most general results known in the Hilbertian case. In particular, we obtain the density under a quadr...