Calculus of Variations and Geometric Measure Theory

E. Durand-Cartagena - A. Lemenant

Self-contracted curves are gradient flows of convex functions

created by durandcar on 20 Feb 2018
modified by lemenant on 01 Dec 2018



Inserted: 20 feb 2018
Last Updated: 1 dec 2018

Journal: Proc. AMS
Year: 2018


In this paper we prove that any $C^{1,\frac{1}{2}}$ curve in $\mathbb{R^n}$, is the solution of the gradient flow equation for some $C^1$ convex function $f$, if and only if it is strongly self-contracted.