Gradient flows of $(K,N)$-convex functions with negative $N$
Functional Analysis
2026-05-25 v2 Metric Geometry
Abstract
We discuss -convexity and gradient flows for -convex functionals on metric spaces, in the case of real and negative . 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 -convex functionals characterized by Evolution Variational Inequalities, including contractivity, regularity, and uniqueness.
Keywords
Cite
@article{arxiv.2412.04574,
title = {Gradient flows of $(K,N)$-convex functions with negative $N$},
author = {Lorenzo Dello Schiavo and Mattia Magnabosco and Chiara Rigoni},
journal= {arXiv preprint arXiv:2412.04574},
year = {2026}
}
Comments
24 pages