Erosion and dilation are two useful operations in convex geometry. For instance, dilating a possibly nonsmooth convex body $\Omega $ yields a smooth convex body bigger than $\Omega $ . Eroding $\Omega $ yields a convex body that is smaller than $\Omega $ . Erosion does not have a smoothing effect but it serves to generate rotundity. The present work studies the action of erosion and dilation on closed convex cones. The definition of both operations must be adapted of course to a conic setting. For simplicity in the exposition, we focus on convex cones that are pointed and solid.
