# Sobolev embeddings with weights in complete riemannian manifolds

## TL;DR

This paper establishes weighted Sobolev embedding theorems and Gaffney's inequality for vector bundles on complete Riemannian manifolds, improving classical results under weaker geometric assumptions.

## Contribution

It introduces weighted Sobolev embeddings and Gaffney's inequality in complete Riemannian manifolds, extending and strengthening previous theorems under weaker geometric conditions.

## Key findings

- Weighted Sobolev embeddings for vector bundles proved
- General Gaffney's inequality with weights established
- Improved classical Sobolev embeddings under weak bounded geometry

## Abstract

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.