Abstract

In this basic notions seminar we take a look at how one can define Sobolev spaces for functions from Riemannian manifolds.

We will briefly revise the notion of the covariant derivative and then find a way for how to make sense of the intuitive definition of the Sobolev spaces.

We collect some properties of these spaces. In the end it turns out that for compact manifolds they are basically the same as their cousins on subspaces of flat space.