Do we have enough examples of Convex Bodies?

Is diversity of our standard examples enough to understand Convexity?

In the talk we demonstrate many different constructions which are analogous to constructions of irrational numbers from rationals. In particular we show how the geometric mean (and lambda-geometric means) may be defined for any centrally symmetric convex compact bodies K  and  T. We also construct  K^a for any centrally symmetric K and -1 < a < 1, and also Log K  for K containing  the euclidean ball D (and K = -K). Note,  the power |a| cannot be above 1 in the definition of power !

 

Based on joint results with Liran Rotem.