Approximability of convex bodies and volume growth in Hilbert geometries.


WALSH, Cormac


The approximability of a convex body measures how quickly the complexity of an approximating polytope must increase as one approximates the body more and more closely.
I will discuss how this quantity is related to another one: the exponential rate of growth of the volume of a ball in the Hilbert metric on the convex body.
This is joint work with Constantin Vernicos.