  In this paper we extend some notions, previously defined for log-concave
functions, to the larger domain of so-called {\alpha}-concave functions. We
begin with a detailed discussion of support functions - first for log-concave
functions, and then for general {\alpha}-concave functions. We continue by
defining mean width, and proving some basic results such as an Urysohn type
inequality. Finally, we demonstrate how such geometric results can imply
Poincar\'e type inequalities.
