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Convex Geometry (Winter Semester 2010/11)

Lecture: Monday 11:30-13:00 AOC 201
Tuesday 11:30-13:00 1C-04
Problem class: Wednesday 14:00-15:30 1C-03
Lecturer, Problem classes Prof. Dr. Daniel Hug
Office hours: Nach Vereinbarung.
Room 2.051 Kollegiengebäude Mathematik (20.30)
Email: daniel.hug@kit.edu

Course description

Convexity is a fundamental notion in mathematics which has a combinatorial, an analytic, a geometric and a probabilistic flavour. Basically, a given set A in a real vector space is called convex if with any two points of A the segment joining the two points is also contained in A. This course provides an introduction to the geometry of convex sets in a finite-dimensional real vector space.

The following topics will be covered:

  1. Geometric foundations: combinatorial properties, support and separation theorems, extremal representations
  2. Convex functions
  3. The Brunn-Minkowski Theory: basic functionals of convex bodies, mixed volumes, geometric (isoperimetric) inequalities
  4. Surface area measures and projection functions
  5. Integral geometric formulas

If time permits, we also consider additional topics such as symmetrization of convex sets or sets of constant width.


This course is suited for everybody with a firm background in analysis and linear algebra.

Lecture Notes


Exercise sheets


  • Gruber, P.M. Convex and Discrete Geometry. Grundlehren 336, Springer, 2007.
  • Schneider, R. Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1993.