Blenders

A blender is a closed convex cone of real homogeneous polynomials that is also closed under linear changes of variable. Non-trivial blenders only occur in even degree. Examples include the cones of psd forms, sos forms, convex forms and sums of $2u$-th powers of forms of degree $v$. We present some general properties of blenders and analyze the extremal elements of some specific blenders.