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.

中文翻译：

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完全黎曼流形中具有权重的 Sobolev 嵌入

我们在完整的黎曼流形中证明了带有权重的 Sobolev 嵌入定理。我们还得到了带权重的一般 Gaffney 不等式。因此，在“弱有界几何”假设下，我们改进了完整黎曼流形中向量丛的经典 Sobolev 嵌入定理。我们还改进了完全黎曼流形中 Gaffney 不等式的已知结果。