Gradient flows of $(K,N)$-convex functions with negative $N$

Abstract

We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-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 $(K,N)$-convex functionals characterized by Evolution Variational Inequalities, including contractivity, regularity, and uniqueness.

24 pages

References in corpus (5)

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Eulerian calculus for the displacement convexity in the Wasserstein distance
• Nonsmooth analysis of doubly nonlinear evolution equations
• Weighted Poincaré-type inequalities for Cauchy and other convex measures