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

2024/12/05 by Schiavo, Lorenzo Dello, Magnabosco, Mattia, Rigoni, Chiara
#49J52 #49Q20 (Primary) #53C23 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2412.04574

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.

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