Sobolev embeddings with weights in complete riemannian manifolds

We prove Sobolev embedding Theorems with weights for vector bundles in a complete riemannian manifold. We also get general Gaffney’s inequality with weights. As a consequence, under a “weak bounded geometry” hypothesis, we improve classical Sobolev embedding Theorems for vector bundles in a complete riemannian manifold. We also improve known results on Gaffney’s inequality in a complete riemannian manifold.