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arXiv · 2412.04574

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

Lorenzo Dello Schiavo·Mattia Magnabosco·Chiara Rigoni
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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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Lorenzo Dello Schiavo, Mattia Magnabosco, Chiara Rigoni. 2024-12-05. Gradient flows of $(K,N)$-convex functions with negative $N$. https://doi.org/10.1007/s00526-025-03187-z

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