English

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

Functional Analysis 2026-05-25 v2 Metric Geometry

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 KK and negative NN. 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.

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

R2 v1 2026-06-28T20:24:51.492Z