Modul

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

The students

• know fundamental combinatorial, geometric and analytic properties of convex sets and convex functions and apply these to related problems,
• are familiar with fundamental geometric and analytic inequalities for functionals of convex sets and their applications to geometric extremal problems and can present central ideas and techniques of proofs,
• know selected integral formulas for convex sets and the required results on invariant measures.
• know how to work self-organized and self-reflexive.

None

1. Convex Sets
   1.1. Combinatorial Properties
   1.2. Support and Separation Properties
   1.3. Extremal Representations
2. Convex Functions
   2.1. Basic Properties
   2.2. Regularity
   2.3. Support Function
3. Brunn-Minkowski Theory
   3.1. Hausdorff Metric
   3.2. Volume and Surface Area
   3.3. Mixed Volumes
   3.4. Geometric Inequalities
   3.5. Surface Area Measures
   3.6. Projection Functions
4. Integralgeometric Formulas
   4.1. Invariant Measures
   4.2. Projection and Section Formula
   4.3 Kinematic Formula

Total workload: 240 hours

Attendance: 90 hours

• lectures, problem classes, and examination

Self-studies: 150 hours

• follow-up and deepening of the course content
• work on problem sheets
• literature study and internet research related to the course content
• preparation for the module exam.