Durand Cartagena, EstibalitzLemenant, Antoine2024-12-032024-12-032019-02-14E. Durand-Cartagena, A. Lemenant, Self-contracted curves are gradient flows of convex functions, Proceedings of the American Mathematical Society 147 (2019), 2517-2531 https://doi.org/10.1090/proc/144071088-6826https://doi.org/10.1090/proc/14407https://hdl.handle.net/20.500.14468/24676The registered version of this article, first published in REVISTA, is available online at the publisher's website: American Mathematical Society, https://doi.org/10.1090/proc/14407La versión registrada de este artículo, publicado por primera vez en REVISTA, está disponible en línea en el sitio web del editor: American Mathematical Society, https://doi.org/10.1090/proc/14407In this paper we prove that any C1, 1/2 curve in Rn, is the solution of the gradient flow equation for some C1 convex function f, if and only if it is strongly self-contracted.eninfo:eu-repo/semantics/openAccess12 Matemáticasjournal articleself-contracted curvesgradient flow equationconvex analysisconvex optimizationconvex extensionanalysis in metric spaces