In the Calculus of Variations, convexity plays a seemingly irreplaceable role.For vectorial problems, however, for good reasons a whole zoo of its generalizations was introduced. It ranges  from notions based on very classicalobservation over explicite, but only partially understood,characterizations to very practical  conditions. Recently a new convexity concept emerged, in differnt research projects fordifferent reasons. We are interested in it, since it describes stabilty ofuniqueness of minimizers under a huge class of pertubations. We'll discuss differences, and particularagreement with other convexity notions for vectorial problems.