discipline 
MSC in
Mathematics, Pure Mathematics, Elective Course

subject 
Analytic
Convexity 
lecturers 
Dr. Károly Bezdek (professor), Dr. Károly Böröczky (professor), Dr. Károly Böröczki Jr. (associate professor), Dr. Balázs Csikós (associate professor), Dr. Gábor Kertész (assistant professor), Dr. György Kiss (associate professor), Dr. Gyula Lakos (teaching assistant), Dr. Gábor Moussong (assistant professor), Dr. László Verhóczki (associate professor). 
credits 
2 
period 
1st semester 
curriculum 
Hausdorff measure, differentiability of convex hyper surfaces,
approximation by polytopes, Cauchy’s integral formula for surface area,
Steiner’s formula for the parallel domain, mean projections, representation
of mean projections with mean curvatures, Steiner symmetrization, isoperimetric
inequality for mean projections, BrunnMinkowski inequality for
compact sets, Mixed volumes, AlexandrovFenchel inequality, applications to
combinatorics, RogersShephard inequality, approximation of convex bodies by
ellipsoids (Dvoretzky theorem, the uniqueness of the John and Löwner
ellipsoid). Compact subgroups of GL(n). Ball’s inverse isoperimetric
inequality, the BlaschkeSantalo inequality. 
literature 
R. Schneider: Convex
Bodies – the BrunnMinkowski theory, Cambridge University Press, 1993. P.M. Gruber: Convex and Discrete
Geometry. Springerverlag, 2006. 
form of tuition 
Two hours of lecture per week. 
mode of assessment 
oral exam 