The main goals of the project are as follows:

- Solve the asymptotic Plateau problem in nonpositively, respectively negatively curved spaces / groups. Analyze solutions and find applications.
- Study conformal changes of spaces with upper curvature bounds and find a new approach to Reshetnyak's theory of surfaces with upper curvature bounds.
- Investigate the analytical, geometrical and topological properties of geodesic surfaces with quadratic isoperimetric inequalities and study the compactification of the class of such surfaces.
- Find optimal isoperimetric inequalities for curves in normed spaces and applications to regularity of minimal surfaces.
- Construct minimal surfaces in metric spaces by topological methods and / or min-max techniques.

## Publications

## Team Members

**Prof. Dr. Alexander Lytchak**

Project leader

Universität Köln

alytchak(at)math.uni-koeln.de

**Dr. Stephan Stadler**

Project leader

Ludwig-Maximilians-Universität München

stadler(at)math.lmu.de