Modul

The module will be completed by an oral exam (about 30 min).

Graduates

• are able to mathematically understand and solve a practical problem;
• can explain important results of the theory of minimal surfaces and apply them to examples;
• are prepared to write a thesis in the field of the theory of minimal surfaces or the calculus of variations.

None

Minimal surfaces are critical points of the area functional and locally minimize its area. They can also be described by having zero mean curvature. In this course we consider two dimensional minimal surfaces in R^3 and discuss their properties. We will use arguments from differential geometry, the calculus of variations, the theory of partial differential equations and functions of a complex variable. Our goal is to prove the classical Plateau's problem.

The course "Classical Methods for Partial Differential Equations" is recommended.

Total workload: 90 hours

Attendance: 30 hours

• lectures, problem classes, and examination

Self-studies: 60 hours

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research relating to the course content,
• preparation for the module examination