Responsible: Christian Bär

This lecture course will introduce to the analysis on manifolds. We will first learn about fundamental analytic concepts such as Sobolev and Hölder spaces of functions on manifolds, linear and nonlinear elliptic differential operators and their regularity theory, the maximum principle and the like. Then we will apply those tools to study two famous problems. Firstly, the Yamabe problem deals with finding a geometrically nice metric on a manifold. More precisely, given any metric we want to apply a conformal change to make it have constant scalar curvature. Secondly, we will prove the positive mass theorem, which has its origin in general relativity theory, for spin manifolds.

The lecture course will be given in English.

Lecture and exercise programme:

All necessary information can be found here: Moodle

Semester (recommendation):

Modul Numbers:
MATVMD824, MATVMD825,MATVMD921, MATVMD922

Required prior knowledge:

Literature:
1. C. Bär: Geometrische Analysis, lecture notes, Potsdam 2008