Given a complete non-compact Riemannian manifold (M, g) with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries G of (M, g) that characterizes the coerciveness of G in the sense of 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 the full range of admissible parameters (Sobolev, Moser-Trudinger and Morrey). We also consider the case of non-compact Randers-type Finsler manifolds with finite reversibility constant inheriting similar embedding properties as their Riemannian companions; sharpness of such constructions are shown by means of the Funk model. As an application, a quasilinear PDE on Randers spaces is studied by using the above compact embeddings and variational arguments.

给定具有某些曲率限制的完整非紧黎曼流形 ( M ,  g )，我们引入了关于( M , g ) 的一组等距G的扩展条件， 它表征G的矫顽力在 Skrzypczak 和 Tintarev 的意义上（Arch Math 101(3): 259–268, 2013）。此外，在这些条件下，紧凑的 Sobolev 型嵌入 à la Berestycki-Lions 被证明适用于所有可接受的参数（Sobolev、Moser-Trudinger 和 Morrey）。我们还考虑了具有有限可逆常数的非紧致 Randers 型 Finsler 流形的情况，它们继承了与其黎曼伴星相似的嵌入特性；这种结构的清晰度通过 Funk 模型显示。作为一个应用，通过使用上述紧凑嵌入和变分参数研究了兰德斯空间上的拟线性偏微分方程。