Self-contracted curves are gradient flows of convex functions

Antoine Lemenant, Estibalitz Durand Cartagena

In this paper we prove that any $C^{1,\alpha }$ curve in ${\mathbb{R}}^n$, with $\alpha \in (\frac{1}{2},1]$, is the solution of the gradient flow equation for some $C^1$ convex function $f$, if…