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, Brunn-Minkowski inequality for compact sets, Mixed volumes, Alexandrov-Fenchel inequality, applications to combinatorics, Rogers-Shephard 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 Blaschke-Santalo inequality.

literature

R.  Schneider: Convex Bodies – the Brunn-Minkowski theory, Cambridge University Press, 1993.

P.M. Gruber: Convex and Discrete Geometry. Springer-verlag, 2006.

form of tuition

Two hours of lecture per week.

mode of assessment

oral exam