Abstract We discuss (K, \!N) (K, N) -convexity and gradient flows for (K, \!N) (K, N) -convex functionals on metric spaces, in the case of real K and negative N. In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaining as values both the positive and the negative infinity. We prove several properties of gradient flows of (K, \!N) (K, N) -convex functionals characterized by Evolution Variational Inequalities, including contractivity, regularity, and uniqueness.
Schiavo et al. (Tue,) studied this question.