A Course on Convex Geometry

The following notes were written before and during the course on Convex Geometry which was held at the University of Karlsruhe in the winter term 2002/2003. Although this was the first course on this topic which was given in English, the material presented was based on previous courses in German which have been given several times, mostly in summer terms. In comparison with these previous courses, the standard program was complemented by sections on surface area measures and projection functions as well as by a short chapter on integral geometric formulas. The idea here was to lay the basis for later courses on Stochastic Geometry, Integral Geometry etc., which usually follow in a subsequent term. The exercises at the end of each section contain all the weekly problems which were handed out during the course and discussed in the weakly exercise session. Moreover, I have included a few additional exercises (some of which are more difficult) and even some hard or even unsolved problems. The list of exercises and problems is far from being complete, in fact the number decreases in the later sections due to the lack of time while preparing these notes.

• Convex sets
• Convex functions
• Convex bodies
• Integral geometric formulas

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