Webrelaunch 2020

Convex Geometry (Wintersemester 2008/09)

Vorlesung: Montag 11:30-13:00 Seminarraum 34
Dienstag 11:30-13:00 Seminarraum 34
Übung: Mittwoch 14:00-15:30 Seminarraum 31
Dozent Prof. Dr. Daniel Hug
Sprechstunde: Nach Vereinbarung.
Zimmer 2.051 Kollegiengebäude Mathematik (20.30)
Email: daniel.hug@kit.edu
Übungsleiter Dr. Mario Hörig
Zimmer Allianz-Gebäude (05.20)
Email: Hoerig@math.uni-karlsruhe.de


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.

Lecture notes in English will be available.


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. 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.


Skriptum images2.jpg



  • Gruber, Peter. Convex and Discrete Geometry, Grundlehren der mathematischen Wissenschaften, vol. 336, Springer, Berlin, 2007.
  • Schneider, Rolf. Convex Bodies: the Brunn-Minkowski theory, Cambridge University Press, Cambridge, 1993.