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Given a complete non-compact Riemannian manifold $(M,g)$ with certaincurvature restrictions, we introduce an expansion condition concerning a groupof isometries $G$ of $(M,g)$ that characterizes the coerciveness of $G$ in thesense of Skrzypczak and Tintarev (Arch. Math., 2013). Furthermore, under theseconditions, compact Sobolev-type embeddings \`a la Berestycki-Lions are provedfor the full range of admissible parameters (Sobolev, Moser-Trudinger andMorrey). We also consider the case of non-compact Randers-type Finslermanifolds with finite reversibility constant inheriting similar embeddingproperties as their Riemannian companions; sharpness of such constructions areshown by means of the Funk model. As an application, a quasilinear PDE onRanders spaces is studied by using the above compact embeddings and variationalarguments.

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