Introduction to the Analysis on Manifolds with Conical Singularities

In these notes, I will recall the central elements of the cone calculus. The focus lies on conically degenerate differential operators and the Laplace-Beltrami operator with respect to a conically degenerate metric as a prototypical example. We will get to know manifolds with conical singularities, the Mellin transform, cone Sobolev spaces, and the notion of ellipticity in terms of the invertibility of the principal pseudodifferential symbol and the principal Mellin symbol. Finally, I will sketch the full cone calculus.