Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups

Abstract Given a complete non-compact Riemannian manifold ( M , g ) with certain curvature restrictions, we introduce an expansion condition concerning group of isometries G that characterizes the coerciveness in sense Skrzypczak and Tintarev (Arch Math 101(3): 259–268, 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for full range admissible parameters (Sobolev, Moser-Trudinger Morrey). We also consider case Randers-type Finsler manifolds finite reversibility constant inheriting similar embedding properties as their companions; sharpness such constructions shown by means Funk model. As application, quasilinear PDE on Randers spaces is studied using above variational arguments.