  In this paper we study properties of the area evolute (AE) and the center
symmetry set (CSS) of a convex planar curve $\gamma$. The main tool is to
define a Minkowski plane where $\gamma$ becomes a constant width curve. In this
Minkowski plane, the CSS is the evolute of $\gamma$ and the AE is an involute
of the CSS. We prove that the AE is contained in the region bounded by the CSS
and has smaller signed area.
  The iteration of involutes generate a pair of sequences of constant width
curves with respect to the Minkowski metric and its dual, respectively. We
prove that these sequences are converging to symmetric curves with the same
center, which can be regarded as a central point of the curve $\gamma$.
